Helge Dyvik

Department of Linguistics and Comparative Literature

Section for Linguistic Studies

University of Bergen
 
 

1. Introduction

A difficulty in evaluating the competing approaches to machine translation (MT) against each other is the lack of a common frame of reference, some principled theory of MT against which various proposals could be evaluated. We have no developed account of machine translation, or of translation in general, that is both reasonably formal and neutral between the various techniques explored in MT research. As John Hutchins points out (Hutchins 1992/1993:261), we need a theory that abstracts away from specific system types. It should be sufficiently formal to allow us to characterise the complexity of a given translation task, or of the translational relationship between two languages, and it should allow us to do so independently of the actual algorithms that one might want to try in solving the task. Thus we cannot build into the theory assumptions about specific representation types, such as tree structures or interlingual representations, or about specific operations, such as structure transformations or transfer-based substitutions. In other words, we need a way to discuss the complexity of translational tasks that abstracts away from both specific grammar formalisms (such as those of Head-driven Phrase Structure Grammar, Lexical-Functional Grammar, Government-and-Binding Theory, etc.) and specific MT system architectures.

How can we approach the development of such a theory? What can be said about potential system types that abstracts away from everything that is not common to them all? In Hutchins’ words you can apparently say "little more than the trite banality that MT is a computational process which relates linguistic objects (texts) in different natural languages which "have the same meaning"" (p. 261). Banality or not, this is probably where we would have to start: by looking at the translational relation between linguistic objects and, furthermore, the information needed to compute it. To avoid tying ourselves to any particular way of representing the objects and computing the relation, we would have to move the focus from formal representations to what the representations represent. We would then have to look at the translational relation purely extensionally, as a relation between sets of expressions or sets of texts (as instantiated in a translational corpus, for instance), and attempt to characterise aspects of the translational relation — such as its complexity — in such extensional terms. On the basis of such a characterisation we might look for patterns that can be exploited in making the computation of the relation as simple as possible. The theory should allow us to explain such things as why translation between closely-related languages is simpler than translation between more distantly-related languages, and thus provide a basis for the development of MT systems that exploit such relatedness. Furthermore it should help us draw the line between what is computable in practice, what is computable only in principle, and what is neither.

The ambition in this article, then, is to talk about syntactic and semantic representations in terms of what they denote rather than in terms of how they look. We may then ask whether something can be concluded about how similar a pair of representations can be, or how different they must be, on the basis of their denotational properties, irrespective of preferred formalism. Such possible similarity or necessary difference among representations have an obvious bearing on the complexity of a translational task. The remainder of this article will present some basic ideas about how this might be achieved.
 
 

2. Languages as structured sets of signs

The goals sketched above rest on the assumption that it is meaningful and possible to distinguish clearly between the formalism and representations of some linguistic theory on the one hand and on the other the linguistic objects, or linguistic ontology, represented by the representations. Suppressing some valid misgivings we will make this assumption here. The linguistic objects to be discussed here are intersubjective; they are objects of common knowledge.¹ Such objects are highly abstract in nature, but in spite of this, everyday language seems able to handle them (as denotata) in a consistent way. Thus, few people will have difficulties with a statement like "There is a word for ‘horse’ in Norwegian, namely, ‘hest’", even though this single "word", whose existence as a unique entity we readily accept as normal language users, bears a very complicated relation to actual, observable linguistic events among speakers of Norwegian. This inspires confidence in the realistic interpretation of words and phrases as types (as opposed to textual tokens): it is not only the many occurrences of ‘hest’ that exist; it is also reasonable to claim that the word itself, as a type, exists as an object of common knowledge. This way of reasoning is easily extended to other linguistic objects, such as the sentence "It is raining", the word form horses, etc. We will refer to such objects as simple and complex ‘signs’.

A sign is an object with many complex properties, some of which are abstracted out and studied by linguists. In other words, a sign is essentially richer than any linguistic description or representation of it can be expected to be: there will probably always be properties of signs that we have not captured in our theories and formalisms, and possibly also properties that cannot be so captured. Two important types of properties of signs are meaning properties (or content properties) and expression properties. The precise delimitation and empirical interpretation of these types of properties will be theory dependent; one way to characterise them would be to say that the meaning properties of a sign are those properties that determine and constrain the possible use of the sign in the conventional performance of linguistic acts (such as asking, asserting, referring, predicating, etc.), while expression properties are those properties that allow signs to be perceived and identified. The individuation of signs is, in accordance with time-honoured structuralist tradition, assumed to be based on pairings of expression and meaning properties. It is a well-known epistemological fact that it is extremely difficult to individuate and characterise meaning properties in an intersubjectively unique way in isolation from particular signs that have these properties, and that to some extent the same is true of expression properties: distinctions of expression must be related to distinctions of meaning in order to be meaningfully discussed. This emphasises the centrality of the pairing of content and expression itself as the constitutive property of a linguistic sign. Only in virtue of such a pairing do the two types of properties become accessible to characterisation in an intersubjectively consistent way. These observations motivate considering the sign an ontological primitive.

A language L is often conceived as a set of sentences, i.e., maximal signs. We will include the non-maximal signs (lexemes, word forms, phrases) in our concept of a language. Hence, a language L is a set, typically infinite, of signs.² The set is structured, since signs may stand in part-whole relations to other signs. The set of sentences of L will then be a proper subset of L. Signs that do not have other signs as parts (e.g., lexemes), are ‘elementary signs’. Under this conception a language can be seen as a partial algebra of signs — partial because it is not closed under its combining operations (typically, some of the combinations of signs in L yielded by the operations will not themselves be members of L).
 
 

3. Meaning properties and translational properties

Signs can be classified according to their properties. We will assume that signs can share properties, both of meaning and expression, with signs in other languages. Hence the extension of a given meaning property is a set of signs that may have members from many languages.

With the wide conception of ‘meaning properties’ suggested in 2 above it lies near at hand to stipulate that the meaning properties of a sign are precisely the set of properties we aim to capture, if we can, in literal translation.³ That is, the translational relation between signs of two languages (interrelating ‘linguistically predictable translations’) is an instance of the sharing of meaning properties across languages. This implies a close connection between the meaning properties and the translational properties⁴ of a sign: two signs in a language L will share translational properties only if they share meaning properties (and hence will share meaning properties if they share translational properties). Of the two kinds of properties the translational properties seem to be the epistemologically more accessible ones: they can be accessed by applying interpretive methods to actual text pairs of originals and their translations — translations produced without any theoretical concerns in mind. Meaning properties, on the other hand, seem less accessible in an intersubjectively consistent way; traditional methods like intuitive judgments on the part of the researcher, evaluation of possible paraphrases etc., have a more subjective character. Given this epistemological asymmetry between translational properties and meaning properties it seems methodologically advisable to try to define (some) meaning properties in terms of translational properties rather than the other way around (as is common). On the basis of such definitions, in which the translational relation is taken as an epistemological primitive or ‘given’, the more accessible translational properties of a sign can then provide a window onto its meaning properties. In Dyvik (1998) these ideas are developed and explored in a corpus-based study. For example, in that article synonymy is defined in terms of shared translational properties, hyponymy in terms of subset relations among translational properties, and ambiguity and vagueness in terms of more complex translational relations between sets of signs.

A consequence of defining meaning properties in translational terms is that the meaning properties thus become relativised to given sets of target languages. Thus, two Norwegian lexemes or sentences may be synonymous with respect to English if they share all possible translations into that language, but not with respect to, say, French, if one has a possible translation into French that is not shared by the other. Two signs would be synonymous tout court if they had the same set of possible translations into all possible target languages. Hence the analysis and description of the meaning properties of a language L — for instance the fine-grainedness or ‘granularity’ of the analysis — will vary with the sets of target languages we take into account. This is clearly the kind of variation we want when the purpose of the meaning analysis is automatic translation: efficient translation performs no more semantic analysis than is necessary in order to find the set of possible translations in the target languages currently relevant.
 
 

4. The denotation of semantic representations

In Dyvik (1998) it is argued that semantic representations should be taken to denote sets of linguistic signs.⁵ This departs from traditional assumptions, whereby semantic representations such as logical formulae in Montague semantics or situation schemata in situation semantics are taken to denote the same model-theoretic objects or objects in the world as the linguistic expressions they are associated with. Under the assumption pursued here, semantic representations denote and hence classify signs according to their meaning properties, while only the signs denoted by the representations denote objects and relations in the world (or in a model of it). Thus a semantic representation is an expression in a technical language which we use to ‘talk’ about linguistic objects (which obviously is the kind of technical language we expect in a discipline like linguistics).

In the construction of semantic representations for machine translation (as interlingua expressions, for instance) the decisions about what kind of information to include in the representations are clearly in practice based on the need to find translations in given target languages: information irrelevant to that purpose is excluded. The assumption that semantic properties of signs are individuated relative to target languages, and that semantic representations denote sets of signs according to their semantic properties, makes this common practice follow from general principles. Adding ‘superfluous’ information to a semantic representation will then not alter its denotation: it will still denote the same set of signs in the languages in question. In other words, the augmented representation will be equivalent to the original un-augmented representation, the addition thus emerging as redundant. Furthermore, extending the set of relevant languages to all possible natural languages we see that the granularity we can achieve in semantic representations is then limited not only by the ‘granularity’ of the world, which is hardly a limitation at all, but by the ‘granularity’ of the world’s languages: we need no more granularity in our representations than is necessary in order to keep the sets of linguistic signs distinct. Hence it is the distinctions that can be drawn in possible natural languages that determine the distinctions we need to draw in our technical languages of semantic representations. Since semantic representations in linguistics in practice tend to be limited in precisely this way, we again have a case of common practice following from revised assumptions about the denotation of semantic representations — in itself an argument in favour of the revised assumptions.

Taking the denotation of semantic representations to be sets of linguistic signs involves giving semantic representations and syntactic representations the same kind of denotation. It is even more obviously plausible to assume that syntactic representations — for example, phrase structure trees or LFG f-structures — denote sets of linguistic expressions than to assume that semantic representations do so. An empty f-structure denotes the full set of expressions in a language — or in any language, if we assume universally interpreted f-structures — and as we add features to it, it denotes gradually diminishing subsets of expressions.

The difference between syntactic and semantic representations will then rest on the kinds of properties of linguistic signs that determine the denoted classes. The kinds of properties relevant to identifying the denotations of semantic representations have already been discussed: they include translational properties. We obviously want syntactic representations to identify syntactic properties of signs, that is, to denote sets of signs that have some set of syntactic properties in common. ‘Syntactic properties’ can be understood as the kind of properties that determine the wellformedness of linguistic signs — the kind of properties you have to refer to in order to justify that a sign is a member of the language in question. In other words, these are the kind of properties that a sentence recogniser will have to know about.

Although our ambition is to remain maximally non-commital towards alternative ways representations may look, we will make the basic assumption that both syntactic and semantic representations can be more or less specified, in the following sense.⁶ We assume that the set of possible representations (syntactic or semantic) have a monotonic structure: representations can combine into more complex representations (or, conversely, they can have material removed from them and thus become simpler representations). Furthermore, we assume that as material is added to a representation its denotation typically shrinks to a subset of its previous denotation. This quite familiar idea can be illustrated by the simple examples in figures 1-3.

The phrase structure trees in figure 1 show an increasing degree of specification from a through d, and, correspondingly, the denotations of the trees in English successively shrink to subsets of the previous denotations. The maximally underspecified S tree in 1a denotes the full set of sentences in the language.

Attribute-value structures are more typically used with varying degrees of specification. The LFG-type f-structures in figure 2 show an increasing degree of specification in a through c, with a corresponding shrinking of the denotation in English. Since only a, but not b and c, subsume d, the denotation of d is a subset of a’s denotation, but not of the denotations of b and c. Furthermore, taking the unification of e with any of a, b, or c, the unification in each case would denote the intersection of the denotations of the representations in question. d and e do not unify, and correspondingly, their denotations do not intersect.

The predicate-argument structures in figure 3 are simple examples of semantic representations, and illustrate the same basic points as figure 2. Thus, for example, c is the unification of a and b and denotes the intersection of the denotations of those two representations.
 

Figure 1: A fragment of the denotation in English of some phrase structure trees

Figure 2: A fragment of the denotation in English of some LFG f-structures

Figure 3: A fragment of the denotation in English of some predicate-argument structures

With this possibility of having semantic (and syntactic) representations with varying degrees of specification, it is clear that a given sign may be in the denotation of many semantic representations. However, we will assume that there will always be exactly one semantic representation that is the full representation of the sign, namely, the one denoting the smallest denoted set of which the sign is a member. We may formulate this as an axiom:

Axiom 1: For each sign a in a language L seen in the context of a set of languages L, there will be a semantic representation s such that a is included in the denotation d of s and for all other semantic representations s’ whose denotations d’ include a, dÃd’.

s is then the full semantic representation of a. Notice that two or more signs may share the same full semantic representation.

For a pair of languages L1 and L2, assume a translational relation t which associates with each sign a from L1 its linguistically predictable translations in L2. This relation will induce a partitioning of L1 whereby the members of each partition are synonymous with respect to L2, i.e., they have exactly the same set of signs in L2 associated with them by the t-relation. We will refer to a set of such synonymous signs in L1 as a T-set. We may then formulate the following axiom ensuring that only synonymous signs share a full semantic representation:⁷

Axiom 2: Assume a language L1 analysed in the context of a language L2 and the translational relation t defined from L1 to L2. For each T-set A Õ L1there will be a semantic representation s that is the full semantic representation of each sign in A and of no other sign in L1.
 
 

5. Parsing and generation

Machine translation systems vary, but they invariably involve both some sort of parsing of a source expression, and some sort of generation of a target expression. The complexity of a translational task may therefore be discussed in terms of the complexity of the parsing and generation required.

A syntactic parser is usually characterised as a recogniser which in addition to determining whether a string is an expression of the language or not also returns a representation of it. To make this definition precise, we have to demand that this representation must be (at least) a syntactic representation in the sense discussed in the previous paragraph: a representation of the properties of the expression that led to the conclusion that the expression was a member of the language. The prototypical parser returns a summary of its calculation of well-formedness.

If this is our conception of parsing and we go on to conceive of generation as the mirror-image of parsing, then generation becomes an almost completely trivial task. A parsing algorithm maps strings to syntactic representations, which presupposes access to a knowledge base of syntactic properties, while a generation algorithm, under this conception, maps syntactic representations to strings, which presupposes no separate knowledge base about the language, since it is just a question of extracting some of the properties already represented in the syntactic representation. For example, generating a string from a phrase structure tree is not much of a challenge. Thus, the starting point for non-trivial (and translationally interesting) generation is not full syntactic representations, but rather semantic representations. As already discussed, semantic representations classify linguistic expressions according to their translational properties.

Since the distinctions drawn in a semantic representation do not presuppose that corresponding grammatical or lexical distinctions are drawn in that particular language (only in some possible source or target language), and since there is no a priori reason why a semantic representation should correspond closely to a syntactic representation of a given expression, generation from semantic representations is a possibly non-trivial and complex task. How complex depends on the degree of correspondence between the semantic and the syntactic representations of the sign whose expression is to be generated. The syntactic and the semantic representations of a sign may be more or less isomorphous: if they are both hierarchic, for instance, it may be more or less the case that the nodes in one representation correspond one-to-one to the nodes in the other, and that corresponding nodes dominate corresponding nodes. Consider, for instance, the non-b-reduced formulae of Montague semantics, which correspond rather closely in their hierarchic structure to the syntactic analysis tree of the sentence which was used to derive them, as compared to the reduced formulae, in which all such syntactic information is lost:

Figure 4: Unreduced and reduced formulae

In figure 4 the complex, non-reduced formula at the top node is derived from the syntactic analysis of the sentence ‘All the students read a book’ (under the reading where they all read the same book). This complex formula contains subformulae that correspond one-to-one to the subexpressions isolated by the syntactic analysis, as can be seen by comparing it with the formulae at the various tree nodes. Thus it happens to contain information about the syntactic structure of the sentence as well. The semantically equivalent reduced formula at the bottom, on the other hand, does not. It is obviously much easier to generate from appropriate non-reduced formulae that from reduced formulae; in the latter case the major problem is precisely finding the desired choice among the infinitely many possible l-abstractions that could be applied, to expand the formula to a form suited to the syntax of the target language. In our context the example illustrates that semantic representations may be designed in many ways, some more suitable for efficient generation in a given language than others.
 
 

6. Implicational relations between syntax and semantics

In short, there is no one mandatory way a semantic representation must look, and one might ask whether it is possible to say anything about the degree of correspondence between syntactic and semantic representations, and hence about the complexity of generation, in abstraction from particular proposals about the way the representations should look. Still, even in the absence of such proposals the possible degree of correspondence between a semantic and a syntactic representation may be partly an empirical question, since it may be the case that the signs denoted by a given semantic representation have widely differing syntactic properties. Thus we may have the picture of figure 5, showing the denotations SEM, SYN1 and SYN2 in the language L1, of the semantic representation sem and the syntactic representations syn1 and syn2:

Figure 5: Different syntactic properties among the signs denoted by a semantic representation

Assuming, now, that there is no syntactic representation with a useful degree of specificity (i.e., with an interestingly small denotation) whose denotation includes the union of SYN1 and SYN2, we have a situation where the signs in the denotation of a semantic representation are divided into groups with quite disjoint syntactic properties. This means that sem can hardly be formally close to both of syn1 and syn2 at once: there can be a trivial mapping from sem to at most one of the two. In such cases generation from semantic representations will be relatively complex.

Since semantic properties are individuated relative to target languages, this circumstance is directly relevant to the complexity of the translational relation between two languages. As an example, consider the following t-correspondence between Norwegian and English:

(1) A: {de vedtak som ble fattet av Stortinget, de av Stortinget fattede vedtak}

--t->

B: {the decisions that were made by Parliament, ...}

There is a stylistic difference between the two Norwegian expressions, the latter (in gloss "The by Parliament made decisions") being more formal than the former. But since (as we assume here) English does not draw a corresponding distinction — so that the Norwegian expressions have the same translational properties with respect to English — they belong in the same T-set and are synonymous with respect to that language. Thus we have a full semantic representation whose denotation contains signs with different syntactic properties, and therefore the semantic representation cannot be formally close to all the syntactic representations involved: a case of the kind illustrated in figure 5. This means that for at least one of the Norwegian expressions the translation from English to Norwegian (or vice versa) would have to be relatively complex.

The question whether there can be a trivial mapping from the semantic to the syntactic representations of a set of sentences, and hence whether generation is trivial or difficult, is thus actually the question to what extent semantic equivalence implies syntactic equivalence for the set of signs denoted by the semantic representation. Such an implicational relationship is illustrated in figure 6, where all the signs denoted by sem are also denoted by syn.

Figure 6: Semantic properties implying syntactic properties

If this is the picture, then it is possible to design the semantic representation in such a way that it corresponds formally to the syntactic representation of the signs, in which case generation from semantic representations will be relatively easy.

We may now proceed to consider how the greater simplicity of the translational relation between more closely-related languages emerges from this picture. Intuitively, translation between closely-related languages is simpler because closely-related languages will share a relatively large number of linguistic "devices". That is, they will to a large extent have similar structures with similar semantic properties. This involves two things: in the first place similar semantic distinctions will be drawn in two closely-related languages, and in the second place the distinctions will frequently be drawn by similar lexical and grammatical means. We will consider these two factors in turn.

To take the point about the similar semantic distinctions first, one consequence of considering a pair of closely-related languages will be that the patterns of synonyms — the partitioning into T-sets — in each language will be influenced in such a way that the situation of figure 5 (where semantic properties are distributed over signs with different syntactic properties) will be more infrequent, and the situation of fig. 6 (where signs sharing semantic properties tend to share syntactic properties) more frequent than in the case of more distantly-related languages. Compare example (1) above, from Norwegian to English, with (2) and (3), from Norwegian to Swedish:

(2) A: {de vedtak som ble fattet av Stortinget,}

--t->

B: {de besluten som fattades av Stortinget}

(3) A: {de av Stortinget fattede vedtak}

--t->

B: {de av Stortinget fattade besluten}

The Norwegian T-set in (1) has been split in two in (2)-(3) because (simplifying slightly) Swedish grammaticalises a similar stylistic distinction as Norwegian, with the consequence that the stylistic distinction can be preserved in translation from Norwegian into Swedish. Thus the two Norwegian expressions are not synonymous with respect to Swedish and hence get different semantic representations sem1 and sem2. In this way we get one semantic property for each syntactic property in the original picture from figure 5; cf. figure 7.

Figure 7: One semantic property for each syntactic property in the analysis of closely-related languages

This obviously simplifies generation from semantic representations, since we may now design our semantic representations in such a way that the mapping to syntactic representations is trivial.

Further simplification results from the second point, that the two languages do not only draw similar semantic distinctions, but that they also do so by similar means. Intuitively, this means that we frequently do not have to find the semantic representation sem and its denoted set SEM in order to pair an expression with at least some of its translations in the closely-related target language; we can restrict ourselves to considering the syntactic properties. In the example just considered the interrelated expressions in Norwegian and Swedish do not only have the same stylistic⁸ properties, they also have the same syntactic properties. Hence, this is a type of case where common syntactic properties across two languages imply common semantic properties: it is relatively frequently the case that the denotation of some syntactic representation shared by the two languages is included in the denotation of some semantic representation with a non-trivial degree of specification. (Thus, for instance, the general syntactic representation of NPs with the complex pre-head structure in (3) will denote a set of signs in Norwegian and Swedish sharing a certain stylistic/semantic property.)

Figure 8 : Syntactic properties implying semantic properties across two languages

In evaluating the complexity of translation, cases where syntactic properties imply semantic properties are even more interesting than cases where semantic properties imply syntactic properties. The obvious reason for this asymmetry is that our ultimate goal is to find the syntactic properties of the sign whose expression we want to generate. Hence, if we already have the syntactic properties (knowing that they imply the semantics we want) we do not need to find the semantic properties as well. But if we have the semantic properties, even knowing that they imply the desired syntactic properties is not enough: we still need to find the syntactic properties in order to generate. Furthermore we may assume that in analysing a source expression, information about syntactic properties is more easily accessible than information about semantic properties. A parser will normally have to find the syntactic representation of an expression in order to calculate its semantic representation, but not vice versa.
 
 

7. Complexity as a function of sparse implicational relations

In general, identification of cases where equivalence with respect to easily accessible properties implies equivalence with respect to less easily accessible properties will be useful in the simplification of the translational procedures. The point is that the translator in those cases only needs to worry about the re-creation of the easily accessible properties — the others will follow by implication. Thus — as discussed above — if a human translator or a system knows that for an identifiable set of cases syntactic equivalence implies semantic equivalence, the translator or the system can safely base the translation on the syntactic structure of the source expression. Consider example (2)-(3) again: If we know that a syntactically equivalent expression in Swedish also is semantically equivalent with the Norwegian expression (i.e., shares a semantic representation with a sufficient degree of specificity), we can base the translation on the syntactic analysis of the Norwegian expression. That is, we can forget about calculating its semantic representation, and we can also forget about consulting the syntactic rules of Swedish. All we need to do is to perform some substitutions within the syntactic representation of the source expression: a rather low-level transfer procedure.⁹

This suggests that we may conceive of the study of the complexity of translation as a study of implicational relations among types of equivalence across two languages. So far we have only considered syntactic equivalence implying semantic equivalence, that is, only properties of linguistic signs as types. If we consider the more immediately given kind of translational relation, namely, the relation between situated texts rather than between linguistic signs seen in abstracto, then further types of equivalence enter the picture, such as connotational equivalence, pragmatic equivalence and text-normative equivalence.

Now, information about the pragmatic properties of utterances is obviously less easily accessible than information about their semantic properties. Thus, any reasonably developed linguistic description will identify a sentence like "Could you close the window?" as an interrogative, and hence the performance of the speech act ‘question’ as the conventional, semantic content of its syntactic structure. However, in an actual text the sentence might be used not only to ask a question, but — more likely, in this case — to make a request, or even to give an order, provided that the relationship between the interlocutors is of a certain kind. It is clearly much more difficult to determine the actual speech act performed — a pragmatic property of the text — than to determine the speech act conventionally associated with a sentence type — a semantic property of the sign used. However, in reasonably related languages, such as Norwegian and English, it will frequently be the case that the same semantic types are used to perform the same types of speech acts. In both languages interrogatives can be used to make requests or give orders, in approximately the same types of circumstances. In other words, for this kind of expressions semantic equivalence largely seems to imply pragmatic equivalence. The consequence for translation is that it won’t be necessary to find the pragmatic properties of the text at all: if the subset of the language for which the implication holds can be identified, the translator can trust the implicational relationship to ensure that whatever pragmatic properties arose in the context of the source text will also arise in the target text. In more distantly related languages, on the other hand, it may not be the case that interrogatives can be used in the same way pragmatically. If so, there will be no implicational relationship between the types of equivalence, and it becomes necessary to determine the pragmatic properties of the source text in order to find an adequate translation. In other words, the translational procedure becomes more complex. This is another instance, then, where equivalence with respect to more accessible properties implying equivalence with respect to less accessible properties facilitates translation.

With this kind of explication of the complexity of translation we can investigate empirically the complexity of the relation in a given text type between two given languages. In order to do that we of course need to develop the definitions of different types of equivalence further than the sketch presented here.¹⁰ With this apparatus we may classify translational correspondences in actual texts, that is, bilingual text corpora consisting of source texts and their translations. On the basis of such data we may study implicational relations between types of equivalence, the amount and kinds of information needed in each case in order to calculate the translational relation, and the degree to which we may expect the translational relation to be calculable by an algorithm in the first place.
 
 

References

* Published in: Hilde Hasselgård and Signe Oksefjell (eds.): Out of Corpora.Studies in Honour of Stig Johansson. pp. 215-230. Amsterdam: Rodopi (1999).

1. The way in which knowledge of these objects is represented in the individual mind is conceived as a different, though obviously interdependent, domain of research.

2.  To spell out this part-whole relation we need to distinguish between sign types and sign tokens, since it is tokens of signs that can be parts of other signs (e.g., a sentence may contain more than one occurrence of the lexeme ‘horse’). These are not textual tokens occurring in space and time, but tokens in the more abstract domain of complex signs. Thus, we need to distinguish between different kinds of sign tokens according to the domain of occurrence of the tokens in question.  These matters will be left aside here, however.

3.  As discussed in Dyvik (1998) the translational relation immediately given in actual translations is a relation between situated texts, or parole items, rather than a relation between signs, or langue items. Among successful actual translations many are motivated by contingencies of the particular text rather than by linguistic properties of the signs translated. By ‘literal translation’, on the other hand, we understand translation restricting itself to the set of ‘linguistically predictable translations’, which can be assumed to be given by a translational relation between the signs of two languages, i.e., between langue items. We assume that such a relation can be extricated by interpretive methods from actual translations.

4.  The translational properties of a sign are given by the set of signs in other languages that are (linguistically predictable) translations of it. Two signs in L that share such a set across all languages will be synonymous, at least for the purpose of translation. See Dyvik (1998) for discussion.

5.  More precisely: representations are taken to denote sets of sign senses in a technical sense explained there, but for present purposes we may think of the denotations as sets of signs.

6.  It follows from this assumption that a ‘semantic representation’ of a sentence does not necessarily contain enough information to determine its truth conditions.

7.  The axiom does not preclude that the full semantic representation of a sign a is also a semantic representation of a non-synonymous sign b, as long as it is not b’s full semantic representation. b will then be a sign with a more specialised meaning than a, and hence a more specified full semantic representation.

8.  Grammaticalised or lexicalised stylistic properties count as semantic properties under our assumptions, since they determine translational properties of signs.

9.  The experimental MT system PONS, developed by the author, exploits closeness of languages in this way; see Dyvik (1995).

10.  For some suggestions see Thunes 1998.
 

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