The main questions I want to address in this chapter are: how can translational phenomena be used as data for the development of linguistic semantics, and why would we want to do so in the first place?

As part of the group studying translational phenomena in the Centre for Advanced Study in Oslo in 1996/97 I have been able to use the bilingual text corpus ENPC developed by Stig Johansson and his colleagues, in which Norwegian originals are aligned with their English translations, and vice versa.¹ The study reported here can be seen as a contribution to the development of a conceptual basis for using such translational corpora as a basis for deriving large-scale semantically classified vocabularies for use in machine translation and other kinds of multilingual processing. But a translational basis for semantic descriptions may be interesting in a wider linguistic context, too. For one thing, translation takes place on a very large scale, and it brings a desirable multilingual perspective into the study of linguistic semantics, which traditionally is heavily monolingual in its scope. For another, the activity of translation is one of the very few cases where speakers evaluate meaning relations between expressions without doing so as part of some kind of meta-linguistic, philosophical or theoretical reflection, but as a normal kind of linguistic activity. This inspires confidence in the intersubjectivity of such evaluations. Furthermore, the activity has what one might call extensional consequences: the result of the translator’s evaluations is manifest in observable relations between texts. This latter point is interesting from a methodological point of view: it contributes to the externalisation of the criteria against which linguistic descriptions should be evaluated. Such externalisation is important in order to strengthen the empirical foundations of linguistics.
 
 

3.2 The Translational Relation

Using translational phenomena as a basis for linguistic descriptions presupposes that it is meaningful to talk about a translational relation between two languages. We want to treat the translational relation as a primitive — as something we can access in texts and in dialogues with bilingual informants. The translational relation, so conceived, is not a relation between abstract linguistic expressions, like for instance synonymy. Rather, it is a relation between situated texts. It interrelates parole items rather than langue items: the actual linguistic expression used is not the only thing which determines what will count as a useful translation. Relevant also are the context of utterance, the purpose of the utterance, and various other kinds of background knowledge.

Semantic properties are properties of linguistic expressions seen as types, not only as tokens in texts. In order to use translations as a source of information about semantics, we therefore need to extricate the contribution that contextual factors such as these make to the translational relation from the contribution made by correspondence relations between words and phrases seen as types. That is, the translational relation we are interested in isolating, is not the one between texts or parole items, but the one between linguistic expressions or ‘signs’ seen as types, that is, between langue items as they occur in grammars or dictionaries. In other words, we unsurprisingly find that corpus data cannot be directly used in raw form. Linguistic data are as usual accessible only through an interpretive process, for instance through dialogues with informants, in this case consisting in "peeling off" two layers of irrelevant data. In the first place we want to disregard "bad translations", thereby isolating instances of the genuine textual translational relation between two languages. In the second place we want to disregard translational choices that can be motivated only by reference to the particular text and its circumstances, thereby isolating the linguistically predictable translations. The linguistically predictable translations will then be the ones that reflect the translational correspondence relations between the sign inventories of the two languages — relations between words and phrases seen as types rather than textual tokens. Defining this relation will then be a question of defining a relation between two languages, seen as structured inventories of signs.
 
 

3.3 The Denotation of Semantic Representations

It seems doubtful that machine translation can ever do much more than calculate the set of linguistically predictable translations of a given expression. Hence it is not surprising that formal semantic analysis is a useful tool in machine translation. The present author has developed and studied an experimental translation system called PONS (see Dyvik 1995). In one of its modes of operation the PONS system uses semantic representations in the form of situation schemata as interlingua expressions (cf. Fenstad & al. 1987). We may consider a somewhat simplified example of a semantic representation derived for the sentence "All the students were reading a book" (fig. 1). The leftmost layer of the structure represents the type of discourse situation conventionally presupposed by the sentence: it is a declarative, and hence we have an INFORM relation holding between speaker, hearer, described situation and discourse location. The discourse situation also has a topic identical with an object in the described situation, the identity being shown by graph unification. In the described situation there is a read’-relation holding between an indeterminate constrained to be anchored to individuals that are arguments of the relation student’ and another indeterminate similarly constrained by the relation book’. The loc substructure shows how the described situation relates temporally to the discourse situation (i.e., it precedes it), and the polarity of the sentence (positive) is represented by the value yes associated with the relation name read’.

Fig. 1 A semantic representation of a sentence

In the present study the situation schema is only intended as a more or less arbitrary example of a semantic representation, but it may be illuminating to consider more carefully what a representation like this should be taken to stand for, or denote. In the explanation just given it was vaguely assumed that it should be taken to denote either things in the world talked about, or slightly more formally, a situation-theoretic object in which we find relation primitives like inform and read, and indeterminate objects whose anchoring is constrained to certain types of individuals (books and students), etc. In other words, it seems initially plausible to take the schema as a simple little picture of a bit of the world. There are two factors that may make us feel uncomfortable with this assumption, however: firstly, the situation-theoretic object we assume "behind" the schema really looks more like a bit of language than like a bit of the world, with verb-like relation primitives like read, book, and student, and secondly, our inventory of representation primitives, and the granularity of the representations, are primarily motivated by the need to find translational partners in other languages rather than by properties of the world talked about. Semantic representations reflect linguistic distinctions, and this is true not only in the context of translation. One purpose of general linguistics, and hence of linguistic semantics is to characterise the limits of variability among possible natural languages. Hence the distinctions we need to draw in our theoretical framework will be closely related to the distinctions that could be drawn in some natural language.

What this suggests is that every putative semantic distinction that our theory allows us to draw should be motivated as a possible lexical or grammatical distinction in some natural language. All semantic distinctions would then be possible lexical or grammatical distinctions. Since languages hence determine how we need to carve things up in our possible worlds, one should in a sense consider possible languages before considering possible worlds. The number of distinctions, or "granularity", we can achieve in semantic representations will then not be limited only by the granularity of the world — which is hardly a limitation at all — but by the granularity of the world’s languages. The claim made here is that this is a principled statement of what we on reflection find that we are actually doing when constructing semantic representations in linguistics.

In order to incorporate these ideas into the theory we may reconsider the question of the denotation of semantic representations. Seeing that what the representations actually do for us is capturing a type of equivalence among linguistic expressions, we may take their basic function to be to classify signs together. In 3.7 below a way to model the concept of a sense of a sign will be proposed, and we will then be able to say that semantic representations denote sign senses. We may then say that a semantic representation classifies together a set of linguistic signs across languages, namely, the set of signs with senses that fall within the denotation of the representation. It will then only be the linguistic signs which, in their turn, denote situations, relations and objects in the world, according to some meaning theory.

Without going deeply into the question of the delimitation of semantics, let us simply assume that semantic properties comprise more than truth-functional properties of linguistic signs (any conventional constraint on the use of a sign associated with the sign as a type will count as a semantic property) and that the semantic properties are precisely the properties we want to preserve in literal translation, if we can. Hence the semantic properties of a sign determine its translational properties.

Thus the translational relation will be central in the determination of the set of signs (or more precisely: sign senses) that is denoted by a given semantic representation. The expression "read’" in the situation schema, then, does not denote a relation in the world, but a set of linguistic signs across languages standing in a certain translational correspondence relation to each other. This set of signs can, in their turn, be taken to denote such a relation if desirable, but that will be a meaning-theoretical question we need not settle in the present context. The meaning of a semantic representation is then fully given by a set of linguistic signs. This being so, we only draw distinctions in our formalism of semantic representations to the extent that this is necessary in order to keep the denoted sets of linguistic signs apart: a distinction is motivated only if the sets denoted are distinct. This implements the idea that all distinctions in the semantic formalism are possible lexical or grammatical distinctions.

It should probably be stressed that there is no suggestion that the study of semantics can be reduced to the study of translational relations among linguistic signs. The claim is rather that translational properties should be seen as an important window onto the semantic properties of signs, providing an empirical foundation for the way in which we describe them. This seems especially worthwhile within the field of lexical semantics. Earlier semantic studies in the tradition after Richard Montague did not have much to say about lexical semantics. The focus was rather on the compositional side of semantics: on the way in which the meaning of larger entities like sentences and phrases can be derived as a function of the meanings of their composite parts and their modes of combination. In these studies the meanings of the smallest elements — the words — were typically unanalysed primitives, like the read relation in the situation structure. Lexical semantics has received increased attention during the last decade,² primarily inspired by the needs of computational linguistics. This makes a more solid empirical foundation for the description of sense relations and other aspects of denotational meaning all the more desirable.
 
 

3.4 Semantic Analysis and the Translational Relation

If we want to bring translational phenomena into the sphere of formal semantics, we need to develop a formal basis for doing so. A common characteristic of different approaches within formal semantics is the use of algebraic methods. Montague semantics and later theories inspired by his work can be seen as spelling out a relation between two algebras. In the case of Montague-type semantics, one partial algebra models the language, and the other algebra models the "world" talked about.

The translational approach identifies translational properties as an additional basis for individuating semantic properties of signs. This can be incorporated into the picture by viewing the algebras of target languages as algebras serving a similar function with respect to the source language as the semantic models do. That is, in a similar way as the meaning of an expression is captured by its relation to certain objects in the semantic model, it can be seen as captured by its relation to certain objects in the target language algebras. We may then go on to look for patterns in these algebraic relations, reflecting semantic properties, as in the case of the traditional semantic models. One advantage of treating target language algebras like this is that whereas the semantic models are constructed by the theorist and hence are very far from being intersubjectively given phenomena, the target languages are more intersubjectively accessible facts of the world. Hence they constitute an "externalisation" of the criteria of adequacy for semantic analyses and thus provide more of an empirical foundation for the study.

The elements of the language algebra will be signs of various types. A sign is a simple or complex element of a language that can be delimited in the traditional way on the basis of expression properties (phonological properties, syntactic properties, distribution etc.) and that has an intersubjectively accessible set of meanings. For present purposes we may think of the sign elements as lexemes, word forms, phrases, sentences and grammatical categories, with certain inclusion relations among them. Thus, under this conception a language is not a set of sentences; it is larger, since it also comprises sentence parts, down to word forms and lexemes, as separate elements, and it is a structured set, with an ordering relation corresponding to ‘part of’ among its elements. For instance, the ordering relation will interrelate a lexeme and its set of word forms (the lexeme being seen as an elementary sign that is ‘part of’ each of its forms) or a phrase and the set of sentences in which it occurs.

The illustrative examples in the present article will mostly concern lexemes. Therefore the question of the exact structure of the algebras may be set aside, and for present purposes we may regard them instead as unordered sets of signs.

The translational relation between linguistic signs, then, is the empirical relation we hope to capture as a relation between such language algebras, in order to discover its patterns. We may characterise this primitive relation roughly as a relation t between L1 — the source language algebra (the signs of the source language) — and L2 — the target language algebra:

Fig. 2 A relation t between the signs of two languages

t = {<a , b> | a is a source language sign, b is a target language sign, and b is an optimal translation of a in some not narrowly restricted set of circumstances}

A given source sign may enter into the t relation with more than one target language sign: a sign may be translated in more than one way. Which ones are the optimal translations may vary with the circumstances (within what we consider to be predictable options from the properties of the sign as a type‚ cf. the discussion above at the end of section 1.2). We may call the full set of translations the set of linguistically predictable translations (LPT) of the source sign.

If we reverse source and target languages, we get a relation t* from L2 to L1. We will assume that t* is the inverse of t, i.e., t* = t-1: iff sign e2 is a possible translation of sign e1, we assume e1 is a possible translation of e2. In other words, we assume that t »t* is symmetric. This assumption may be challenged on empirical grounds, but it hardly distorts the empirical picture seriously.

However, we will not assume that t » t* is transitive. Thus, assume that the signs s1 and s2 are members of L1, and t1 and t2 are members of L2. Furthermore, assume t(s1 , t1), t*(t1 , s2), t(s2 , t2). This does not imply t(s1 , t2). For example, Norwegian ‘kompani’ may be translated into English as ‘company’; ‘company’ may be translated back, inter alia, as ‘følge’, and ‘følge’ may be translated back again as ‘train’. This does not imply that Norwegian ‘kompani’ kan be translated into English as ‘train’, which indeed it cannot. Hence, even though t »t* is symmetric, it is not an equivalence relation.

A translationally based semantics cannot distinguish semantically between sign senses that do not have different translational properties. If we restrict attention to two languages L1 and L2, then, we may stipulate that in that pair of languages, for each set A from L1 and B from L2 such that A comprises every sign in L1 that have exactly B as its LPT-set, there should be a semantic representation that is the full semantic representation of one sense of exactly every sign in A. The reason is that the members of A by definition have the same translational properties, and hence semantic properties, with regard to L2.

Synonymy means having the same full semantic representation, and the concept of a full semantic representation, as we have seen, will be relative to a given set of target languages. Thus the relevant senses of the members of A, which by definition have the same full semantic representation as long as only the target language L2 is taken into account, will be synonymous with respect to L2. In other words, synonymy becomes a relativised concept: Full synonymy would mean identical translational properties with respect to all possible target languages, while relative synonymy will hold with respect to subsets of target languages. This accords well with the seemingly paradoxical observation that full synonymy does not seem to occur, while the concept of synonymy still is indispensable in semantic studies. This, then, is an instance of the externalisation of criteria: Even if we intuitively feel able to describe minute meaning differences between the members of a set of signs in a language, this does not legitimise giving them distinct semantic representations unless we can also demonstrate that they have different translational properties with respect to a relevant set of target languages.
 
 

3.5 Ambiguity, Vagueness and t-images

Ambiguity (i.e., the association of two or more distinct meanings with a sign³) and vagueness are a traditional couple of problematic concepts both in lexical semantics and in grammar, and it is an interesting question whether the two properties leave different imprints on the pattern of translational relations. In the next section we will examine some cases of lexical ambiguity and vagueness. They seem to share the basic pattern of fig 3 (which is also the pattern of underspecification⁴). We may add a few words to the diagram to illustrate an intuitively clear case of ambiguity:

Fig. 3 The pattern of an ambiguous word ‘grunne’

The two languages here are Norwegian and English. The Norwegian verb ‘grunne’ is etymologically a merger of two entirely unrelated verbs, which accounts historically for the ambiguity between the meaning ‘speculate’ and the meaning ‘found’. (The case is analysed as ambiguity rather than homonymy based on the principle of maximising polysemy; cf Lyons 1977.)

Let us explore the intuition that this is a clear case of ambiguity. What characterises genuine ambiguity is that it is in some sense "accidental" — it is a contingent property of a word in a language that it happens to be associated with two or more different meanings. Therefore we do not expect to find the same ambiguity duplicated by signs in a number of different languages. The multiple possibilities arising from ambiguity are an accidental property pertaining to the way a given language happens to be. The multiple possibilities of vagueness, on the other hand — like in the adjective ‘good’ — seem to have more to do with what is being denoted. Vague words denote a family of things that have something in common irrespective of language. Different objects describable as ‘good’, such as books and wines, may be more precisely described as ‘entertaining’ or ‘tasty’, respectively, but they still share some family resemblance (‘positive quality’) in virtue of being ‘good’. Therefore it is to be expected that vague words are often matched by words that are vague in similar ways in other languages.

In order to examine how this may be reflected in the translational patterns we will define some useful concepts. Assume two languages L1 and L2 interrelated by a translational relation t» t*, t from L1 to L2 and t* from L2 to L1.

• Definition 1: The ‘first t-image’ in L2 of a sign a in L1 is the largest set B of signs in L2 such that for all b Œ B, t(a , b). That is, the first t-image is the LPT-set mentioned earlier — the set of linguistically predictable translations.

• Definition 2: Let T be the first t-image in L2 of a sign a in L1. The ‘inverse t-image’ of a with respect to L2 is the set of first t-images in L1 of all the members of T. That is, the inverse t-image of a with respect to L2 is the set of sets of signs in L1 which we obtain when we find the LPT-set of each member of a’s LPT-set in L2. The sets in an inverse t-image necessarily have a non-empty intersection containing at least the sign a, since t » t* is symmetric.

• Definition 3: Take the union U of all the sets that constitute the inverse t-image of a sign a in L1 with respect to L2. The ‘second t-image’ in L2 of a is a set which includes the first t-images in L2 of the members of U-{a}. That is, we remove the original sign a from U, and then find the first t-images in L2 of the remaining members of U. In addition we include the subset of a’s first t-image that contains L2 signs that have singleton first t-images in L1 (necessarily the singleton set {a}), if any such signs exist. More formally: Let U be the union of the sets in a’s inverse t-image, and let FLn be a function that assigns to a sign its first t-image in language Ln. Then a’s second t-image is the set of sets:

The second component of this definition (after ») — the condition about the L2 signs that have singleton t-images — is necessary in cases where a has one or more correspondents in L2 that do not correspond to any other L1 signs apart from a. (If there are more than one such L2 sign, then these L2 signs will be synonymous with respect to L1 by definition.) Such cases may occur in technical terminologies, for instance. Since we exclude a from the union U in Definition 3 we need to take special care of such cases, since otherwise the second t-image of a would not contain any sets corresponding to that special sense of a.

The reason why we exclude a from the union U is that we want to base the individuation of distinct senses of a on the overlap relations in its second t-image. Including the first t-image of a itself in a's second t-image would ruin this, since then all the sets in the second t-image would necessarily be connected directly or indirectly by overlap relations.

The second t-image of a lexeme a will obviously contain many signs that have nothing to do with the meaning of a, since many of the signs in the first and inverse t-images may themselves be ambiguous. Our interest in the secoind t-image concerns the structure of overlapping subsets which it imposes on the first t-image. Therefore we proceed to define a restricted version of the second t-image of a sign:

• Definition 4: The ‘restricted second t-image’ in L2 of a sign a in L1 is the second t-image in L2 of a restricted to the members of the first t-image in L2 of a. That is, we get the restricted second t-image of a when we remove all the words that are not translations of a from the sets in a’s unrestricted second t-image. It is clear that all those sets must have non-empty intersections with a’s first t-image, since t » t*is symmetric.

Armed with these concepts we may proceed to consider what consequences the intuitive properties of ambiguity and vagueness may have for the patterns of translational relations. Returning to the example in fig. 3: if ‘grunne’ is genuinely ambiguous, we expect the members of its first t-image in English to belong to at least two groups that have little in common semantically. However, the first t-image itself obviously does not reveal this — it is simply a set of lexemes.

Proceeding to consider the inverse t-image we expect to see certain consequences of such a partition into two meanings. If the members of the first t-image were closely related semantically, or near-synonyms, we would expect their first t-images back in L1 to overlap. Obviously their intersection will contain ‘grunne’ anyway, since ‘grunne’ is necessarily a member of all sets in its inverse t-image, whether it is truly ambiguous or not. However, it is worth noting whether the intersection of the two sets in the inverse t-image contains any other lexemes than ‘grunne’ — which would have indicated possible semantic closeness of ‘speculate’ and ‘found’.

If ‘grunne’ is truly ambiguous, we expect that the other lexemes in its inverse t-image belong to at least two semantically distinct sets. This ought to have consequences for the overlap patterns in the second t-image of ‘grunne’, when we make our third translational movement and consider the first t-images of all these other lexemes. Thus, if the sets in the (restricted) second t-image of ‘grunne’ form n groups in such a way that the sets within each group are connected by overlap relations, while no overlap occurs between the groups, then this indicates n distinct senses of ‘grunne’, each such group corresponding to one distinct sense. If we are considering the properties of the lexeme universally, we should put it more carefully: such a pattern does not allow us to reject the hypothesis that ‘grunne’ is n-way ambiguous rather than just vague between the alternatives, but the hypothesis may be tested and rejected by considering alternative target languages, which might yield more overlap relations. On the other hand, we may also relativise the concept of ambiguity (as we have done with synonymy) and say that with respect to the given target language, n-way ambiguity definitely obtains.

If the target language should contain a lexeme l which is ambiguous in the same way as the lexeme we are investigating, the groups in the second t-image will overlap in l and thus "falsely" give the impression of non-ambiguity. But as we have discussed, such duplication is untypical of ambiguity, which typically is an accidental property of a sign in a language. Therefore we expect such cases to be rare, and to be identifiable by extending the set of target languages — provided, again, that we are studying the lexeme in a universal context. But relativised to just the particular target language such a case would be indistinguishable from vagueness.

Within each sense there will typically be vagueness. The normal case is that a lexeme has a number of different possible translations, which in their turn have more or less different translational properties when we consider the inverse relation. Absence of vagueness in a lexeme sense would then mean that all the translations corresponding to that sense are synonymous (or, as a special case of this, that there is only one possible translation).

Based on these connections between the intuitive concepts of vagueness and ambiguity on the one hand and translational patterns on the other, we may proceed to formulate extensional definitions of ambiguity and vagueness.

Examples will be discussed in the next section.

Vagueness is a property of a sense of a sign, and not directly of the sign itself. Thus, an ambiguous sign can have one vague and one non-vague sense. Vagueness is the normal case; therefore we define the special case non-vagueness:

• Definition 6: A sense m of a sign s in L1 is non-vague with respect to L2 iff every member of the union U of the sets in the group corresponding to m (by Definition 5) has exactly the same first t-image in L1 — that is, iff U is either a singleton set or all members of U are synonymous with respect to L1.
 
 

3.6 Three Case Studies

As a first exploration of the consequences of the definitions in the preceding paragraphs we will examine the translational properties of three Norwegian lexemes in the Norwegian-English corpus (ENPC — see footnote 1). In the present section we will apply the definitions in order to identify cases of ambiguity. In the following section (3.7) we will proceed to discuss the characterisation of the different senses of the lexemes, and introduce new definitions for that purpose.

In what follows, the identification of translational correspondents of lexemes in the corpus is based on the author’s evaluation of the examples — which, it must be said, mostly have been fairly straightforward in that respect. The procedure has been as follows: Given a lexeme l in L1, a search for all occurrences of forms of l was carried out in the corpus of original L1 texts and of L1 translations. Each occurrence was presented in the context of its sentence, paired with the sentence (or sequence of sentences) that corresponds to it in the translation of the text into L2, or the original in L2, respectively. The author then identified the lexeme (or other sign) corresponding to l in the translation. The following types of examples were disregarded:

• Non-literal translations in which l has no identifiable correspondent at all;

• Idiom-like cases (where the original or the translation is idiom-like) in which the correspondence clearly is non-literal.

• Cases where l is part of a phrase that corresponds to a single lexeme in L2 — i.e., cases where the corresponding lexeme does not correspond to l alone in the L1 text.

The starting point for excerpting correspondences has been the three lexemes discussed below: Norwegian ‘tak’, ‘selskap’ and ‘god’. This means finding the translational correspondences for these three lexemes in English (starting both from originals and from translated texts), the translational correspondences of the set of English lexemes thus encountered, and finally the translational correspondences of the new Norwegian lexemes thus added. The total number of lexemes investigated (i.e., registered with their full set of correspondents) as a result of this is 246 — whereas the total number of lexemes found is 925.

Obviously the relative frequency of the various correspondences of a lexeme would be relevant for many purposes and also could have been a criterion for disregarding examples. Frequency has not been considered here, however; the purpose has simply been to examine the set of possible translations and see what patterns can be derived from them. Still, we will identify some problems that follow from disregarding frequency completely.
 
 

Example 1: Norwegian ‘tak’

Historically the Norwegian noun ‘tak’ is a merger of two Old Norse neuter nouns, ‘?ak’ = ‘roof’ and ‘tak’ = ‘grip’. (Since there are no formal distinctions between the two meanings in Modern Norwegian we analyse this as a case of polysemy, and not as a case of two homonymous lexemes, in accordance with the principle of maximising polysemy in the individuation of signs; cf. Lyons 1977.) Fig. 4 shows the first t-image of ‘tak’ in English (restricted to ENPC) in the right-hand box, and the union of the sets in its inverse t-image in the left-hand box.

Fig. 4 The first t-image and the union of the sets in the inverse t-image of ‘tak’ with respect to English (restricted to ENPC)

Fig. 5 shows the overlap patterns among the sets in the inverse t-image.

Fig. 5 The inverse t-image of ‘tak’

The overlap patterns in fig. 5 already indicate a division into different senses. Disregarding the word ‘tak’ itself (which necessarily occurs in all the sets and hence cannot help us identify non-ambiguity), we can distinguish three disjoint groups of directly or indirectly overlapping sets, the word ‘grep’ (= ‘grip’) uniting one of them and the word ‘hvelving’ (= ‘vault’) the other, while the third group consists of the single large set on the left. Still, as we see in Definition 5, we do not distinguish between senses on the basis of the inverse t-image, but on the basis of the restricted second t-image. This is basically an arbitrary choice; the two kinds of definition would necessarily yield the same number of senses (with some provisos not of relevance here).

Taking the first t-images of all the words except ‘tak’ in fig. 5 (and adding the singleton sets of any words in ‘tak’s first t-image that are only related to ‘tak’ — none in the example) we get the second t-image of ‘tak’:

{{hold working_hours work time status situation service score role post position job employment appointment}

{cover way team stratum party line layer incrustation group company class}

{roof ceiling vaulting vault arch}

{hold grip grasp control}

{cover turnabout compress change}

{cover file briefcase}

{hold roots}

{roof loft}

{roof peak}

{cover lid}

{cover shelter}

{cover shed}

{cover hiding-place}

{cover thicket}

{ceiling}

{grip}

{cover}}

It is obvious that the second t-image contains many words that have nothing to do with the meaning of ‘tak’, but occur as a result of ambiguities in other words in the inverse t-image. Thus, for instance, ‘employment’ occurs as a result of the ambiguity (or vagueness?) of ‘stilling’ (translating ‘hold’), while ‘team’ occurs as a result of the ambiguity of ‘lag’ (translating ‘cover’). The interest in the second t-image primarily lies in the subset structure it imposes on the first t-image. Therefore we disregard all words in the second t-image that are not members of the first t-image, thus arriving at the restricted second t-image of ‘tak’:

{{ceiling roof}

{grip hold}

{hold}

{cover}

{roof}

{ceiling}

{grip}}

Fig. 6 displays the overlap relations in the restricted second t-image.

Fig. 6 The restricted second t-image of ‘tak’

According to Definition 5 we conclude that Norwegian ‘tak’ is 3-way ambiguous with respect to English as restricted to the ENPC. We have the following ‘sense groups’:

Group 1:

{{cover}}

Group 2:

{{grip hold}

{grip}

{hold}}

Group 3:

{{ceiling roof}

{ceiling}

{roof}}

This is in accordance with intuitions to some extent, but not fully: we would probably have wanted to see the ‘cover’ meaning included among ‘roof’ and ‘ceiling’. In order for this to happen, ‘cover’ and ‘ceiling’, or ‘cover’ and ‘roof’, would have to share a translation into Norwegian apart form ‘tak’. It does not seem unlikely that such a common translation might be found in a larger corpus. Hence we see that the limitations of a corpus may lead us to distinguish too many senses of a sign.

The overlap structure within each group will form the basis for describing the senses of signs by means of semantic representations; this will be discussed in section 3.7.

The sense groups induce a partitioning of the first t-image of ‘tak’: if we take the unions of the sets within each group, this set of unions will constitute non-overlapping and jointly exhaustive subsets of the first t-image:

{{cover}

{grip hold}

{ceiling roof}}
 
 

We will refer to these subsets of the first t-image as the sense-partitions of it.
 
 

Example 2: Norwegian ‘selskap’

It may not be intuitively obvious whether the noun ‘selskap’ should be described as ambiguous or vague. Among other things it may be used to refer to a festive gathering, and to a limited business company. Opinions may differ as to the semantic relatedness of the two.

Fig. 7 shows the first t-image (to the right) and the union of the sets in the inverse t-image (to the left) of ‘selskap’ with respect to English, based on the ENPC.

Fig. 7 The first t-image and the union of the sets in the inverse t-image of ‘selskap’

Fig. 8 shows the patterns of overlap in the inverse t-image.

Fig. 8 The inverse t-image of ‘selskap’

In the inverse t-image the noun ‘selskap’ itself is included in a singleton set, which indicates that at least one of the members of the first t-image corresponds only to ‘selskap’. Disregarding ‘selskap’ we see that the sets form two overlap groups, one consisting of the single set {sosietet sirkler samfunn}, and the other of three sets, where the intersections contain ‘firma’, ‘bedrift’ and ‘lag’. It is worth noticing that the existence of a word like ‘lag’ has the consequence of bringing the ‘festive gathering’ and the ‘business company’ types of meaning together within one vague sense rather than having them as alternative senses. This makes (and I apologise for the pun) sense: the existence of more than one sign with the same meaning potential ought to mean that ambiguity becomes less plausible as a conclusion, since typical ambiguity is a fortuitous property of a sign, as discussed above. The existence of a similarly ambivalent sign in the target language would have the same effect.

The restricted second t-image of ‘selskap’ is as follows:

{{company party}

{company firm (N)}

{party}

{company}

{society}

{firm (N)}

{companionship}}

The overlap relations are illustrated in fig. 9:

Fig. 9 The restricted second t-image of ‘selskap’

This gives the following sense groups, according to Definition 5:

Group 1:

{{companionship}}

Group 2:

{{society}}

Group 3:

{{company firm (N)}

{company party}

{firm (N)}

{company}

{party}}

The sense partitions of the first t-image, then, are:

{{companionship}

{society}

{company firm (N) party}}

‘Companionship’ is the word that is only found corresponding to ‘selskap’ and nothing else in the corpus. Unless we discard such examples because of low frequency of occurrence (‘companionship’ occurs only once in the corpus), this by definition constitutes one sense of ‘selskap’, as in "Han sørger for hyggelig selskap" = "He provides good companionship". Intuitions about the relationship between this meaning and the ‘party’ meaning may differ, but the conclusion does not seem totally unreasonable. The isolation of the ‘society’ sense, as in "det gode selskap" = "high society", seems even more plausible.
 
 

Example 3: Norwegian ‘god’

The adjective ‘god’ (= ‘good’) is the prototypical example of a vague lexeme covering a vast range of shades of meaning according to context and collocations. The quantitative reflex of this in the present study is the rapid increase in number of lexemes as we proceed from first through inverse to second t-image: the first t-image has 41 members, the union of the members of the inverse t-image has 165 members, and the corresponding union of the second t-image has 638 members. Hence we shall dispense with Venn diagrams in this case.

The first t-image of ‘god’ is:

{able affectionate all_right attractive beneficial bright clear comforting delicious easy excellent fair favourable fine firm (A) first-rate fortunate fresh friendly full genuine good kind nice peaceful pleasant plentiful positive ripe satisfactory serviceable sizeable solid sound spectacular steady superb sweet tantalising thorough worthy}

The union of the sets in the inverse t-image of ‘god’ is:

{ålreit ærbar alle_tiders alvorlig artig attråverdig attraktiv bastant behagelig bemerkelsesverdig beroligende betryggende blank blid bra brav deilig dekkende direkte dugelig dyktig dyp effektiv egentlig ekte elskverdig enestående enkel fantastisk fast fersk fin firskåren flink flott førsteklasses fordelaktig forekommende forjettende fornuftig fortrolig fredelig fremragende frisk full fullspekket gedigen glimrende gløgg god godmodig grei grundig gunstig hel heldig høy høytidelig holdbar hyggelig imponerende inntagende iøynefallende ivrig jevn kjærlig klar klartenkt komfortabel konstant koselig kraftig kvikk lekker lett lettvint levende liflig liten lokkende lykkelig lys lysende massiv moden munter ny nydelig nyhogd nykokt nyplukket opplagt oppmuntrende oppriktig oppsiktsvekkende oppvakt overlegen pålitelig passelig pen perfekt positiv praktfull praktisk prima reell ren rettferdig rik rikelig riktig rimelig rolig seriøs sikker sindig sjarmerende skarp skikkelig skinnende skråsikker smilende snill søt solid solrik spektakulær sterk stø stødig stor storartet strålende sunn superb suveren sympatisk tett tilfredsstillende tiltalende tiltrekkende trivelig trøstende trygg tung tydelig tynn uforstilt ulidelig utmerket utsøkt våken vakker varm vedvarende veldedig vellykket vennlig vennligsinnet vennskapelig verd verdig viktig virkelig ypperlig}

The restricted second t-image of ‘god’ contains 95 sets; the 20 largest of them are printed below:

{{good nice fine sweet attractive excellent easy}

{good nice pleasant sweet friendly all_right kind}

{nice fine pleasant sweet attractive fair}

{good nice fine pleasant sweet attractive}

{good fair thorough spectacular sizeable}

{good fine bright clear firm (A)}

{good bright solid sound thorough}

{good nice fine bright attractive}

{good bright sweet fresh all_right}

{good nice fair satisfactory genuine}

{good nice fine easy all_right}

{solid clear steady firm (A)}

{pleasant sweet friendly kind}

{bright clear fresh fair}

{solid steady firm (A) positive}

{good solid sound thorough}

{nice fine sweet delicious}

{nice pleasant friendly kind}

{good fine all_right beneficial}

{good nice fine all_right}

...}

According to Definition 5 the restricted second t-image is divided into five sense groups by overlap relations:

Group 1:

{{ripe}}

Group 2:

{{tantalising}}

Group 3:

{{serviceable}}

Group 4:

{{worthy}}

Group 5:

{{good nice pleasant sweet friendly all_right kind}

{good nice fine sweet attractive excellent easy}

{good nice fine pleasant sweet attractive}

{nice fine pleasant sweet attractive fair}

{good nice fine easy all_right}

...

[80 sets skipped]

...

{good}

{fine}

{solid}

{fresh}

{genuine}

{easy}}

Sense groups 1 - 4 all consist of single singleton sets, which suggests that they may represent spurious "senses" as a result of a low frequency of occurrence of the relevant words, or at least of the relevant correspondences. Again, a frequency filter might have removed them, but we include them here for completeness. Apart from those singleton groups — probably an inevitable consequence of a fairly small corpus — the result indicates that sense individuation may fruitfully take place based on overlap relations in the second t-image.

Thus we end up with the following sense partitions of the first t-image of ‘god’:

{{ripe}

{tantalising}

{serviceable}

{worthy}

{able affectionate all_right attractive beneficial bright clear comforting delicious easy excellent fair favourable fine firm (A) first-rate fortunate fresh friendly full genuine good kind nice peaceful pleasant plentiful positive satisfactory sizeable solid sound spectacular steady superb sweet thorough}}
 
 
 
 

3.7 Semantic Fields and Sense Descriptions

We will now turn to the question of how the individual senses of a sign may be described, for instance for the purpose of automatic translation. Let {P1, ..., Pn} be the set of sense partitions of the first t-image in a language L2 of a sign a. Since the sense partitions correspond one-to-one to the senses of a, we will model the senses of a sign (with respect to L2) as ordered pairs consisting of the sign and one sense-partition of its first t-image in L2. The senses of a, then, will be represented by the set of ordered pairs <a , P1>, ..., <a , Pn>. Thus, the senses of ‘selskap’ are represented by:

<selskap , {companionship}>

<selskap , {society}>

<selskap , {company firm (N) party}>

After having individuated senses in this manner, we may talk about the first t-images of sign senses, and not only about the first t-images of signs. The first t-image of a sign sense <a , P1> will be the partition of the first t-image of a that corresponds to it — i.e., P1.

We may use the concepts defined so far to try to capture the notion of a semantic field. Traditionally a ‘semantic field’ is a kind of meaning continuum which the signs of different languages tend to carve up in different ways. A semantic field is like a large, vague potential "sense" which is not necessarily the sense of one sign, but rather the joint "sense" of a set of semantically related signs. We will expect such a set of semantically related signs in a language L1 to have overlapping translational properties with respect to a target language L2. Hence we may try to define the sets of lexemes belonging to the same semantic field on the basis of the t-relation. However, saying that two signs a and b in L1 belong to the same semantic field if they have overlapping first t-images in L2 will not suffice, since the shared L2 sign s may be ambiguous between an ‘a-sense’ and a ‘b-sense’ with no close relationship between them. But if it is, then a and b will not belong to the same sense partition of s’s first t-image in L1. Therefore we can exclude that possibility in the definition:

• Definition 7: Two sign senses <a , P>, <b , Q> in L1 belong to the same semantic field with respect to L2 if either (i) there is an L2 sign xŒ P « Q whose first t-image in L1 has a sense partition R such that aŒ R and b Œ R, or (ii) there is a sequence of sign senses in L1 with <a , P> as its first member and <b , Q> as its last member, in which each consecutive pair of senses is interrelated as described in (i).
 
 

3.7.1 Ranking of Signs in a Semantic Field

The subset structure of a sense group, such as that of group 5 for ‘god’ above, clearly reflects semantic relationships among the signs involved. If we rank the lexemes in group 5 according to the number of subsets in which they occur, we arrive at the hierarchy below. It is worth noticing that this hierarchy is derived quite independently of frequency of occurrence (except that a lexeme of course has to occur at least 32 times in the corpus in order to be a member of 32 subsets); it is only based on overlap relations among t-images:

32: {good}

18: {nice}

15: {fine}

14: {bright}

12: {pleasant}

10: {solid}

9: {sweet}

8: {attractive friendly}

7: {clear excellent fresh sound}

6: {fair steady}

5: {all_right easy firm (A) full satisfactory thorough}

4: {comforting kind positive}

3: {beneficial delicious genuine}

2: {able affectionate favourable first-rate fortunate peaceful

spectacular superb}

1: {plentiful sizeable}

The hierarchical pattern indicates that the subset structure reflects significant properties of the semantic field covered by the signs involved. Clearly, the lexemes occurring in the highest number of subsets are the ones with the most ‘general’ or ‘prototypical’ meaning among the possible translations of Norwegian ‘god’. The highest-ranking signs are the ones that have the widest range of translational possibilities within the sense concerned, which, it intuitively seems, must be associated with a wide "meaning potential" as compared to the lower-ranking signs. This may mean that they have a kind of ‘prototype’ status vis à vis the lower-ranking signs, or that they are somehow ‘underspecified’ in relation to them, as hyperonyms to hyponyms — we will return to the exact nature of the semantic relationship.

It should be stressed, however, that the ranking above only takes the number of subsets in which a lexeme occurs into account, and not the extent to which the subsets actually are hierarchically related to each other. That will clearly be relevant for establishing whether a hierarchical relationship obtains or not between two given signs. We will return to different kinds of subset structures below; at this point we will simply define what it means for two signs to be hierarchically related to each other in a structure of sets:

• Definition 8: In a set of intersecting sets an element a is ‘ranked relative to’ an element b iff there is a set A such that a Œ A and b Œ A. a is‘ranked higher than’ b iff a is ranked relative to b and the number of sets X such that a Œ X exceeds the number of sets Y such that b Œ Y. a is ‘uniquely ranked higher than’ b iff a is ranked higher than b and there is no set A such that a œ A, b Œ A.

In the context of machine translation, for instance, it is obviously of interest to be able to identify hierarchical semantic relationships. Thus, if the search for a close translational equivalent fails for some reason — the closest equivalent might be contextually inappropriate, for example — it is desirable to be able to search for an alternative with a ‘wider’, ‘less specified’, or ‘more prototypical’ meaning. (If a certain object — say, a beach — cannot felicitously be described as ‘friendly’ or ‘attractive’ in English, we may at least call it ‘pleasant’.) Information about hierarchies like the one indicated above may be useful for that purpose. To make that information available, we may design the semantic representation of the individual sign in such a way that the hierarchical structure of the sets in the relevant sense groups is implicitly reflected in it. This can be done in the traditional way by allowing the semantic representations to be marked in varying degrees, so that high-ranking signs with ‘wide’ meanings have representations that are less marked than low-ranking signs with more ‘narrow’ or specialised meanings.
 
 

3.7.2 Deriving Semantic Representations: Basic Ideas

Semantic representations are taken to denote sets of sign senses, and we will assume that the representations can monotonically grow into more complex (i.e., marked) representations, their denotations typically shrinking to subsets of previous denotations as they do so. Thus, when we have a pair of sign senses a and b that are hierarchically interrelated in the way discussed above, with a as the higher-ranking one, there should be a representation r1 that includes both a and b in its denotation, and another, more complex, representation r2 that includes only b, the more specialised sign sense, in its denotation. Furthermore, by letting the simple r1 be the full semantic representation of a, and the more complex r2 the full semantic representation of b, the hierarchical relationship is implicitly reflected in the representations assigned to the sign senses.

Feature matrices are simple examples of such representations, and we will proceed to discuss how semantic representations in the form of feature matrices can be derived from translational properties as reflected in the hierarchical structure of sense groups.⁵

A strongly impoverished version of the largest sense group in the restricted second t-image of ‘god’ will serve as an illustrative example during the following discussion. Fig. 10 shows a small subset of the union of the inverse t-image in the left-hand box, and the corresponding subset of the second t-image of ‘god’ in the right-hand box. The focal sign ‘god’ itself, and the relevant subset of its first t-image, have been added in boldface to the images in fig. 10 to mark the borderline between the second t-image and the restricted second t-image of ‘god’. Thus, the restriction of the five images of ‘fin’, ‘nydelig’, ‘hyggelig’, ‘deilig’ and ‘snill’ to the elements within the boldface ‘god’ area belong to the restricted second t-image.
 
 

Fig. 10 A subset of sense group 5 of ‘god’

For the sake of readability we also give the sets in fig. 15 in list form below, with a vertical stroke in each list separating the signs within the first t-image of ‘god’ from the others:

fin: {attractive easy excellent fine good nice sweet | beautiful delicate great lovely smart well-made wonderful}

nydelig: {delicious good nice | beautiful charming cute lovely}

hyggelig: {friendly nice pleasant | cozy disarming lovely polite}

deilig: {delicious fine nice sweet | beautiful delightful enchanting lovely}

snill: {all_right friendly good kind nice pleasant sweet | gentle}

In addition to reflecting hierarchical semantic structure we also want the semantic representations to enable us to recover all possible translational correspondences of a given sign. This means that all pairs of signs that are interrelated by t must share at least one feature. A straightforward way to achieve this — but a way which would not take the hierarchical structure of subsets into account — would be to construct one feature fi for each pair of signs a and s such that t(a , s), and then assign fi to the relevant sense of a, to the relevant sense of s, and to the senses of all other signs synonymous with those two, but to no other signs apart from these.⁶ This would mean that fi would denote the set {a , s} (plus their synonyms), and that the number of features assigned to any sign sense would be equal to the cardinality of the relevant sense partition of the sign’s first t-image. Thus, using the notation [a|s] to represent the feature constructed from a pair of signs a and s such that t(a , s), the relevant sense of ‘god’ would then be assigned the features in fig. 11, based on the relations in fig. 10:

<god , s5>

{[god|excellent], [god|attractive], [god|easy], [god|fine], [god|good], [god|nice], [god|sweet], [god|delicious], [god|all_right], [god|kind], [god|friendly], [god|pleasant]}

Fig. 11 Redundant assignment of features to a sense of ‘god’

[god|excellent] would then also be associated with ‘excellent’, [god|fine] with ‘fine’, etc. Each feature would denote a small number of signs — usually two, in the absence of synonyms. ‘God’ would be in the denotation of all the features, and the intersection of all the feature denotations would probably contain just ‘god’.

However, as already indicated, this feature assignment principle fails to take the hierarchical information into account. The hierarchical structure should be reflected in the degree of specification in the representations, i.e., in the relative number of features associated with the signs. In general, the higher the rank of a sign, the smaller the number of features associated with it will tend to be (while the feature assignment principle we just rejected would lead to the inverse correlation: the higher the rank, the more features, since high rank means a large first t-image). When we go on to consider this, it is important to keep in mind the distinction between the pair of signs that a feature f is constructed from (and which is reflected in its arbitrary name above), and the set of signs whose senses a feature denotes, which may be larger. The names of the features are entirely arbitrary and could have been replaced by numbers or other symbols, but we stick to the convention already introduced for ease of exposition, since it is sometimes necessary to refer to the signs from which the feature was constructed.

The subset structure in fig. 10 imposes a strongly hierarchical structure on the signs involved. In fact, there is one sign, ‘nice’, which is a member of all subsets. This means that all the other signs in the group are ranked relative to, and uniquely lower than, ‘nice’. Hence this is an exceptionally clear case.

Assuming that we have thus identified the highest-ranking signs, ‘god’ and ‘nice’, on both sides in this network of t-relations, we proceed to construct a feature from them:

[god|nice]

This feature is now to denote the two signs ‘god’ and ‘nice’, and a number of other signs that are ranked lower than, and hence are assumed to have more specialised meanings than, these two signs. As discussed above, we assign the feature to the relevant senses of the signs in its denotation. In the first place the feature is associated with ‘god’ and ‘nice’ themselves:

<god , s5> <nice , si>

[god|nice] [god|nice]

Then we associate the feature with all signs ranked lower than ‘nice’ in the sense group: ‘sweet’, ‘pleasant’, ‘delicious’, ‘friendly’, etc. Similarly we associate the feature with further Norwegian signs, namely, all signs in the restricted second t-image of ‘nice’ in Norwegian that are ranked lower than ‘god’.⁷ In the example this will include all the signs in the left-hand box in fig 10: ‘fin’, ‘nydelig’, ‘hyggelig’, etc.

The relevant senses of the two signs ‘god’ and ‘nice’ are not assigned any further features: [god|nice] is their full semantic representation, whereas the other signs that have now had this feature associated with them, may receive more features as we move on. This captures the central or ‘prototypical’ status of ‘god’ and ‘nice’ within the sets of signs considered. It also means that ‘god’ and ‘nice’ are classified as (sense-wise) synonyms in this simplified case.⁸

In this way hierarchical semantic properties are taken care of, but we also need to be explicit about the way in which the feature assignments capture the translational properties. The feature assignment principle we are discussing can be seen as imposing a measure of closeness on the t-relation: some of the pairs interrelated by t appear to be more closely associated — to be closer translational matches — than others. The measure is based on the number of shared features as a fraction of the total number of features associated with the signs: the more shared features, the closer the translational match. Thus, in the example ‘god’ and ‘nice’ are perfectly matched, since they share all features (in casu one). On the other hand, a sign like Norwegian ‘hyggelig’, after having received more features as discussed below, will be less closely related to ‘nice’, which only carries a subset of the features associated with ‘hyggelig’. Translating ‘hyggelig’ with ‘nice’ will thus appear as a case of de-specification. Still, the possibility of this translation is captured by the fact that ‘hyggelig’ and ‘nice’ share the feature [god|nice].

Notice, however, that the fact that an L1 sign a and an L2 sign s share a feature is not a sufficient condition for the t-relation to hold between them. By the feature assignment procedure outlined so far, signs like Norwegian ‘snill’ and English ‘delicious’ also share the feature [god|nice], but they do not stand in the t-relation to each other. Intuitively, the point is that ‘snill’ and ‘delicious’ both have more specific semantic properties than the properties expressed by the feature [god|nice], and they do not share these more specific properties. In the case of ‘nice’, however, the feature [god|nice] is among its most specific features (in fact, its only feature), and therefore this feature can capture its trelation to other signs, such as ‘hyggelig’. Now, by our naming convention for features we express informally this special relationship between a feature and the signs of which it is a most specific feature: the signs from which a feature f is constructed are, by our feature assignment principles, precisely the ones of which f is a most specific feature. Therefore we can formulate the principle by which the t-relation is captured in the feature analysis as follows:

• Feature expression of the t-relation: The t-relation holds between two signs a and s iff they share a feature that is constructed from at least one of them, i.e., by our naming conventions, a feature with a name either of the form [a|x] or of the form [x|s], where x is the name of an arbitrary sign. If a and s share such a feature, we will say that they share a (translationally) crucial feature.

Hence sharing the feature [god|nice] captures the t-relation between ‘hyggelig’ and ‘nice’, because the feature is a crucial feature for this pair, but the sharing of the same feature [god|nice] does not capture any t-relation between ‘snill’ and ‘delicious’, since the feature is not crucial for the latter pair. However, the feature does capture the t-relation between ‘snill’ and ‘nice’, and the t-relation between ‘delicious’ and ‘god’.

If translationally interrelated signs share features over and above the crucial feature(s), this will be a measure of the ‘closeness’ of the translational match.

To assign further features to the lower-ranking signs, we may proceed down the hierarchy, always looking for the highest-ranking signs on both sides. The left-hand box in fig. 10 does not show the subset structure of the inverse t-image, but let us simply select on the basis the largest set in the right-hand box, which is the first t-image of ‘fin’: {attractive easy excellent fine good nice sweetbeautiful delicate great lovely smart well-made wonderful}

The task now is to take care of the translational relation between ‘fin’ and each of these signs. The relation between ‘fin’ and ‘nice’ is already taken care of by the feature [god|nice] associated with both. True, it is also associated with many of the other signs, but as we have discussed, that does not "count": a feature captures the translational relation between two signs a and s fully only if it is constructed from at least one of them.

We should now choose the next highest-ranking sign in order to construct a new feature. To do this, we should consider the second t-image of ‘fin’, which is not shown in full in fig. 10, where we just see the relevant subset of the second t-image of ‘god’. Still, to keep this expository example simple, let us remain with the picture in fig. 10. Among the remaining signs (within the first t-image of ‘fin’) the highest-ranking one is ‘lovely’. We therefore construct our next feature:

[fin|lovely]

The feature [fin|lovely] is now associated with ‘fin’ and ‘lovely’, and further with all English signs in the restricted second t-image of ‘fin’ that are ranked lower than ‘lovely’, and all Norwegian signs in the restricted second t-image of ‘lovely’ that are ranked lower than ‘fin’. In the right-hand box in fig. 15 this means the following signs: {attractive easy excellent fine good sweet beautiful delicate great lovely smart well-made wonderful}. ‘Fin’ and ‘lovely’ receive no further features. This means that ‘fin’ now has the following full semantic representation:

<fin , sn>

[god|nice]

[fin|lovely]

‘Lovely’, on the other hand, being outside the first t-image of ‘god’, only receives the feature [fin|lovely].⁹
 
 

3.7.3 Feature Assignment Principles

The feature assignment principles sketched above can be spelled out more carefully as follows; see Dyvik (forthcoming) for examples and further discussion.

To assign semantic features to the senses of the signs in two languages L1 and L2 in order to capture their semantic properties as induced by the t-relation between L1 and L2, proceed as follows:

3.8 Hyperonyms and Prototypes

The structure, or "topography", of semantic fields may apparently vary considerably, although there are clearly restrictions, worth closer study. (There are obviously even closer restrictions on the degree to which the structures of corresponding semantic fields in L1 and L2 may differ from each other.) The structural variation arises because the sets in a semantic field may overlap to different extents. Two extreme cases are illustrated in fig. 12:

Fig 12 Two kinds of overlap structures

Actually, in order to meet the definition of a semantic field (and not be split in more than one semantic field) a structure cannot be quite as simple as B in fig. 12, while a structure like A can only occur if at least two of the signs involved are synonymous.¹¹ Fig. 13 illustrates approximations we may have to these kinds of structures.

Fig 13 Different overlap structures as they may occur in a coherent semantic field

In a structure like A in fig. 13 there are signs, a and b, that are ranked above all other signs; all the signs are arranged in an approxomate ranking hierarchy with respect to each other. In B, on the other hand, there are many "peaks", or local maxima, and not one sign that is ranked higher than all the others.

Recall that the fact that two signs belong to the same set means that they have at least one common translation in the other language. This suggests a closer semantic relationship between, say, a and f in A in fig. 13 than the one between signs such as a and e, or even more, a and m, in B in fig. 13. a and m do belong to the same semantic field, but the relation between them is mediated by a series of intermediate sets, i.e., by a sequence of signs in the other language uniting the semantic field by means of intransitive overlap relations among their first t-images.

In other words, a structure such as A suggests that there is a semantic relation of increased specification as we move down the hierarchy: the lowest-ranking signs have only a subset of the possible translations of the highest-ranking signs, but they share translations with them (translations that will necessarily be high-ranking in the other language). Hence, signs like a and b in A in fig. 13 will tend to have the quality of hyperonyms with respect to the other signs (like ‘nice’ as compared to either ‘delicious’ or ‘kind’). The more a semantic field structures like A, the more we expect it to have the quality of a hyperonym-hyponym hierarchy. By the feature assignment principles, all the signs in a structure like A will share at least one feature, which intuitively captures the "meaning component" that is shared by the members of such a hierarchy.

A structure like B in fig. 13, on the other hand, suggests that different low-ranking signs (like c and i) may share semantic propertes with a sign that is ranked higher than both of them (like f) without sharing semantic properties with each other, since there is no set that contains both of them — which means that they do not have a common translation in the other language. Hence, a sign like f in B in fig. 13 will tend to have the quality of a prototype with respect to the lower-ranked signs, sharing different properties with different signs.¹² The more a semantic field structures like B in fig. 18, the more we expect it to have the quality of a prototype structure with one or more prototypes surrounded by a "periphery" of signs sharing semantic properties with one or more prototypes, but not necessarily with each other. By the feature assignment principles the peripheral signs in a structure like B might share features with the same prototype, but not with each other. Thus, peripheral signs like c and i in B have no common features, but they have features with overlapping denotations: each will contain a feature that includes the prototype f in its denotation. This captures the fact that the connection between c and i within the semantic field hinges on the existence of a ‘prototypical’ sign like f.
 
 

3.9 The Semantic Significance of Features

The construction and assignment of features, as described in 3.7, are fully based on the patterns of t-relations among the signs involved. Referring to such features as ‘semantic features’ rests on the assumption that our primitive t-relation closely reflects semantic properties of the signs, and that the feature assignment principles come close to factoring out these properties from the t-relations. To the extent that semantic properties are intersubjectively accessible and describable independently of t-relations, independent semantic descriptions may serve as a basis for testing our assumption: we would like to be able to evaluate the adequacy of the feature assignment principles against some independent characterisation of meanings.¹³ For this to be possible we need to be more explicit about the intended relationship between the features and meaning properties.

Semantic theories differ, but some concerns are shared by many of them such as, for instance, the characterisation of entailment relations among sentences or utterances. Keenan and Faltz (1985) show how this and other common concerns of meaning theories can be captured within the conceptual framework of Boolean algebras. A Boolean algebra is a set of elements (including two special elements picked out by 0 and 1) with the three operations Ÿ (meet), / (join) and * (complementation) defined on them.The meet and join operations define a partial ordering on the elements of the algebra: (a Ÿb = a) Æa£b; (a / b = b) Æa£ b.

If an expression A entails an expression B, this intuitively means that A is at least as informative as B: Bruce is a moose is more informative than Bruce is an animal, which it entails, and similarly with red-haired policeman vs. policeman, etc. If the expressions are given denotations in a Boolean algebra, the denotation of the more (or at least as) informative expression would be £ to the denotation of the less informative expression (cf. Keenan and Faltz 1985, p. 7). In a "sets-of-individuals" realisation of the algebra as a simple, first-order model, this would mean, for instance, that the denotation of red-haired policeman would be a set of individuals that is a subset of the denotation of policeman. In a possible-world semantics, the denotation of the proposition Bruce is a moose would typically be a subset of the set of possible worlds that constitute the denotation of the proposition Bruce is an animal. In a situation-semantic analysis, the interpretation of an utterance Bruce is a moose might be a sub-collection of the collection of situations that constitute the interpretation of an utterance Bruce is an animal in the same discourse situation — again an instantiation of a Boolean ordering relation.

The point of using Boolean algebras in this context, then, is that they allow us to say no more than we need. They enable us to remain non-committal towards alternative ontological assumptions and at the same time discuss structural properties that semantic values under the different assumptions would have in common.

In section 3.4 the point was made that the translational approach to semantics can be brought into the sphere of formal semantics by treating target languages in a similar way with the treatment of semantic models. In model-theoretic semantics the meanings of expressions are captured in the relations between two algebras: the language algebra with expressions as elements, and the model, with individuals etc. as elements. The translational approach, too, tries to capture meaning properties by investigating the relations between two algebras — two language algebras in this case (in previous sections simply treated as unordered sets of lexemes, since lexemes are all we have been concerned with here). This, of course, is not meant to replace traditional models: there is no suggestion here that the study of meaning can be reduced to the study of translational relations, only that it can be fruitfully supplemented by such a study, especially within the field of lexical semantics. The question that needs to be addressed, therefore, is how we integrate the insights from the translational study with the insights from the model-theoretic study. This will at the same time address the question above about how to relate the results of the translational study — the feature assignments, or semantic representations — to the constructs of meaning theories.

The basic idea is that the results of the translational study, manifest in the semantic representations, should be seen as imposing constraints on the set of possible semantic models for the languages. By the feature assignment principles, a noun like ‘animal’ would typically be assigned a subset of the features assigned to a noun like ‘horse’. This intuitively captures entailment relations among signs: x is a horse entails x is an animal, etc., since the semantic representation of ‘animal’ is part of the semantic representation of ‘horse’. The relationship can be spelled out as constraints that will only allow semantic models for the language that honour these entailment relations, i.e., semantic models in which the denotation of ‘horse’ is ordered as less than the denotation of ‘animal’: D(horse) £ D(animal). Such constraints are discussed in Dyvik (forthcoming), serving to justify calling the features discussed in this chapter ‘semantic features’.
 
 

Notes

*  Published in: Stig Johansson and Signe Oksefjell (eds.): Corpora and Crosslinguistic Research: Theory, Method and Case Studies, pp. 51-86. Rodopi (1998).

1. The ENPC corpus contains fiction as well as non-fiction. 28 original fictional texts and 15 or 16 original non-fictional texts from each language are represented and aligned sentence by sentence with their published translations into the other language. The total size of the corpus, including originals as well as translations, is 2,257,500 running words.

2.  See , e.g., Pustejovsky (ed.)1993, and Pustejovsky and Boguraev (eds.) 1996.

3.  Thus, ‘ambiguity’ is here taken in the sense of ‘contrastive ambiguity’  rather than ‘complementary ambiguity’ or ‘logical polysemy’, as described in Pustejovsky 1991 and briefly in Pustejovsky and Boguraev 1996, p. 6.

4.  For the distinction between ambiguity, vagueness, and underspecification, see Pinkal 1996.

5.  Intuitively, analysing the meaning of a sign such as an adjective into features involves analysing the property it denotes into a complex of more elementary properties. The basis here, however, is extensional translational relations among signs, and we postpone the discussion of to what extent the feature analysis we arrive at can be given a plausible interpretation in such terms.

6.  When ambiguity is not the issue, we will henceforth sometimes simplify by talking of assigning features to signs rather than sign senses, and of features denoting sets of signs rather than sets of sign senses.

7.  More precisely: all the signs that are ranked lower than ‘god’ in the set of sets we obtain if we add the first t-image of ‘god’ to its restricted second t-image. In the individuation of different senses we needed to exclude the first t-image from consideration for reasons discussed above, and therefore it was excluded in the definition of restricted second t-image. In the derivation of features, however, we are considering semantic fields, where no such exclusions are made.

8.  In the actual, large sense group based on the corpus, there is no one English sign that occurs in all the subsets. This means that there are English signs that are not ranked at all with respect to the highest-ranking sign ? ‘good’ in the actual case. Such signs are not associated with the feature in question, and additional features must take care of their translational relation to ‘god’, which hence will not have the same full semantic representation as ‘good’ or ‘nice’.

9.  This status of ‘lovely’ is probably the result of an accidental gap in the corpus, since ‘lovely’ must be a possible translation of ‘god’. It is possible to define a heuristic procedure on the basis of the t-relations in the corpus to fill such gaps. The basic idea of the procedure is that a sign which is found in the first t-images of sufficiently many "friends and relations" of a sign a ? i.e., of sufficiently many signs in a’s inverse t-image ? can be included in a’s own first t-image. Such a procedure is defined and tested in Dyvik (forthcoming).

10.  I.e., the restricted second t-image of the relevant sense of pk1 augmented with its first t-image.

11.  If no two signs in a structure like 12 A are synonymous, then the signs can be arranged in a sequence in such a way that the first t-image of each sign (except the first) is a proper subset of that of its predecessor. But then there will necessarily be at least one target sign that is translationally related to only one sign in the putative semantic field. This would constitute a sense of its own of the source sign in question (cf. the definition of second t-image), and hence lead to exclusion of that target sign from consideration. If, however, the two highest-ranking signs are synonymous, i.e., if they have identical first t-images, this would not happen.

12. The notion of a prototype can be illustrated with the Vietnamese classifier trái, which classifies fruits and round things, like balls. The prototype uniting the semantics of this classifier is a round fruit, like an orange. Still, the classifier also classifies bananas and footballs, which do not share any relevant property with each other, but rather share one property each with the prototype, ‘fruitness’ and roundness, respectively.

13. Davis and Papcun 1987 is an example of a theory of semantic fields based on speaker evaluations of the semantic distance between lexical items. It would be interesting to investigate the degree of correlation between results obtained in that way and results obtained on the basis of translational relations
 
 

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