On Compositionality and Bidirectional Optimization
Year: 2007
Type: article
Abstract: In this paper we revisit the semantic principle of compositionality and argue that compositionality is bidirectional optimization.Underspecification approaches to natural language interpretation generally start with an underspecified or weak meaning, which is strengthened by contextual information.By contrast, the bidirectional optimization approach we advocate proceeds from the strongest possible meaning.This meaning can be changed or weakened by contextual information.Under this approach, the meaning of an utterance is composed in a functional rather than a concatenative way, while contextual sources of information play a major role.Yet, because the context of any utterance is in principle the same for the speaker and the hearer, composition and decomposition proceed hand in hand.Hence, bidirectional optimization ultimately guarantees (functional) compositionality. The Principle of CompositionalityOne of the key principles in formal approaches to natural language interpretation is the principle of compositionality, which expresses the idea that the meaning of a complex * We thank three anonymous reviewers and Chungmin Lee for their stimulating comments and questions.Helen de Hoop and Petra Hendriks gratefully acknowledge the Netherlands Organisation for Scientific Research (NWO) for financial support of their research.expression can be derived from the meanings of its parts and the way these parts are syntactically linked.That is, a syntactic structure can be mapped onto a semantic structure in which the meanings of the elements of that structure are inserted.This principle of compositionality guarantees that syntax and semantics go hand in hand as each syntactic combinatorial rule is associated with a semantic one.For example, the meaning of a determiner is defined as a two-place relation between two sets of individuals.In the sentence Most cats are black, the set of cats (C) is thus related to the set of black individuals (B) by the determiner most.The sentence Most cats are black is true if and only if the cardinality of the intersection of these two sets exceeds the cardinality of their difference.That is, the sentence is true if there are more cats which are black than cats which are not black.In a formula: most CB is true iff |C B| > |C-B|.This semantic rule can be generalized to all sentences of the form Most AB where A and B represent the two sets of individuals related by the determiner most.Where do these sets of individuals come from?In accordance with the semantic principle of compositionality, they are assumed to come with the syntactic structure of these sentences.In sentences of the form Most NP VP (where NP stands for 'noun phrase' and VP for 'verb phrase', the predicate), the NP refers to set A (also called the domain of quantification) and the VP to set B. The sentence Most black cats have some sort of white spot on them is syntactically decomposed as Most [black cats] NP [have some sort of white spot on them] VP and thus set A is the set of black cats, while set B is the set of individuals that have some sort of white spot on them, and semantically the sentence is true if and only if there are more black cats which have some sort of white spot on them (set A B) than black cats which do not have some sort of white spot on them (set A-B).Other Views on Compositionality Smolensky (1991) notes that "It would constitute significant progress to be able to reduce the (symbolic) principle of semantic compositionality to more basic connectionist principles (…).Developing such a connectionist semantics might well involve formalizing the weak notion of compositionality."With weak compositionality Smolensky refers to compositionality in an "approximate" sense: a non-concatenative way of combining contextually dependent (representations of) elements of a compound expression.Smolensky's (1988) discussion of the (in)famous "cup with coffee"-example may serve to illustrate the point.Note that if the meaning of "cup with coffee" would have been built up compositionally, then we may expect in a connectionist model that the activity vector representing "cup with coffee" would be composed of the vectors representing "coffee" and "cup".However, as Smolensky points out, the pattern representing "coffee" in the context of "cup" is quite different from the pattern representing "coffee" in the context of "can".Roughly, the distributed semantic representation of "cup with coffee" should involve the activation of features such as 'brown liquid with curved sides' or 'brown liquid contacting porcelain' which are not 'part of' the representation of "cup".Hence, if we extract the representation of "cup" from the representation of "coffee" then these features would still be activated, and therefore the remaining activity vector does not represent a contextindependent concept of "coffee" but crucially "coffee in the context of cup".Thus, the representation of "coffee" is context-dependent.Its internal structure is influenced by the structure of which it is a part.Smolensky (1991) calls this weak compositionality: The activation vector consists of 'parts' which influence each other.In that sense, Smolensky's weak compositionality is reminiscent of Frege's (1884) contextuality principle, cited in Janssen (1997): "A word has a meaning only in the context of a sentence, not in separation."Obviously, this latter idea of compositionality conflicts with the thesis of context independency (cf.Hintikka, 1983, cited in Janssen, 1997): "The meaning of an expression should not depend on the context in which it occurs."It should be noted that Smolensky's conception closely resembles what many neurobiologists have in mind when they talk of neuronal assemblies.Smolensky, thus, expresses a still very popular view.A potential problem with weak compositionality is that it does not automatically render systematicity (Blutner et al., 2004).Van Gelder (1990) distinguishes between concatenative and functional compositionality.He describes the essence of a concatenative mode of combination informally as "a way of linking or ordering successive constituents without altering them in any way as it forms the compound expression."For example, tokens of the symbol "P" are the same whether appearing standing alone, P, or in the context of an expression such as (P&Q).Yet, although formal languages of mathematics, logic, and computer science are all compositional in this concatenative sense, concatenation is not the only way of implementing the combination of elements in getting a compound expression.Van Gelder (1990) points out that functional compositionality can be obtained whenever there are general, effective, and reliable processes for (a) producing an expression given its constituents, and (b) decomposing the expression back into those constituents.Whereas concatenative schemes are always functionally compositional as well, it is possible to have merely functionally compositional schemes that are not concatenative.One useful example for a coding scheme that is merely
Source: Journal of Cognitive Science
Language: English
Subfield: Language and Linguistics
Field: Arts and Humanities
Domain: Social Sciences
Open Access status: hybrid
Awards: Asymmetries in Grammar, Animacy
OpenAlex ID: W2163493502