A new hypothesis on compositionality

In this paper we put forward a new hypothesis on compositionality of meaning, namely 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. In contrast, the bidirectional optimization approach we advocate proceeds from 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. Hence, this approach avoids a number of well-known empirical problems associated with concatenative compositionality. Styles of Compositionality 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). Obviously, the thesis of context independency is based on this type of compositionality (cf. Hintikka, 1983, cited in Janssen, 1997): “The meaning of an expression should not depend on the context in which it occurs. ” 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 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 expression can be derived from the meanings of its parts and the way these parts are syntactically linked. Smolensky (1996) 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. In that sense, Smolensky’s weak compositionality is reminiscent to Frege’s (1884) contextuality principle, cited in Janssen (1997): “A word has a meaning only in the context of a sentence, not in separation. ” Compositionality and the Role of Context Notoriously, there are a number of empirical problems with the semantic principle of compositionality. For example, compare the sentence Most people sleep at night to the sentence Most people drink at night. Although the syntactic structures of these two sentences are absolutely identical, the preferred (default) interpretations differ truth-conditionally. The preferred reading of the first sentence can be paraphrased as “At night, most people sleep” whereas the preferred reading of the second sentence is not “At night, most people drink” but rather, “Most people who drink (alcohol), drink at night”. Because these sentences have the same subject, namely most people, at first sight they appear to express conflicting assertions about what most people do. However, they can be simultaneously true in a certain situation for a certain set of people, even if noone of this set of people drinks and sleeps at the same time. In a situation when half of the people drink (they are drinkers) and 80% of these drinkers only drinks at night, the sentence Most people drink at night will be judged true. In the same situation, the sentence Most people sleep at night can be true as well, namely if the people who don’t drink at night (that is, the nondrinkers as well as the day-drinkers), sleep. These two sentences can be true in the same situation because they have different preferred readings. The above two sentences were presented out of context. Because the sentences were presented in written form, no clues were provided with respect to their intonational structure. In addition, their syntactic structures are completely identical. Nevertheless, different preferred readings arise for these sentences. We conclude that in the absence of further context, intonational clues and syntactic differences, these different preferred readings arise as the result of the differences in lexical content in relation to our world knowledge. Although these different readings actually involve different truth conditions, there is no structurally based, mechanical way in which the correct interpretations can be derived. Therefore, sentences like the two above are considered a problem for the principle of compositionality. The above two sentences are quantificational in nature: they contain a quantificational determiner, in this case most. Quantificational determiners are known to establish a relation between two sets. The first set, the domain of quantification, is generally expressed by the noun (together with possible modifiers of the noun) with which the determiner forms a syntactic constituent. However, it can be argued that context always restricts this domain of quantification. Hence, in order to calculate the truth conditions of a quantificational expression, one always has to take into account the context. The truth conditions of a sentence such as Most people drink depend already on what subset of people counts as the domain of quantification of most. Usually, a sentence like this will not be about people in general but rather about some relevant subset of people determined by the context. Obviously, a sentence such as Most of them drink will have varying truth conditions depending on what them refers to. And if the sentence Most drink is uttered out of the blue, the hearer even totally depends on the context in order to determine the relevant set of individuals for the quantifier to live on. At this point, consider the sentence Most drink AT NIGHT. Here, the capitals indicate the accented part of the sentence. If we want to derive the interpretation of this example sentence compositionally, we must assume the presence of an empty noun. The content of this empty structure denotes the whole domain of individuals and gets intersected with a context set variable (cf. Westerståhl, 1985). But in fact, we need two context set variables then. One would be equated with the generalized union over the set of alternatives for the syntactic argument that contains the sentential accent, or focus (cf. de Hoop & Solà, 1996), so that the quantificational domain would be the set of individuals who drink at certain times. The other one would be equated with some additional context set, for example, the set of linguists in Sydney. Hence, in this case we get as the domain of quantification the set of drinking linguists in Sydney. But how many contextual restrictions can or should we add before we may calculate the truth conditions of a quantificational sentence? The question arises when, how and to what extent hearers use different guiding principles to arrive at the proper interpretation of a quantified expression in a given context. As we have seen, different readings do in fact involve different truth conditions. Therefore, we may say that the problem for compositionality just pointed out is a major problem for linguistic theory. Compositionality and Optimization The problem of compositionality, as we pointed it out in the above discussion, is stated by Dekker and van Rooy (2000) as follows: “(.) we cannot systematically determine the semantic content of a sentence in a compositional way based on its syntactic structure, without making reference to the attitudes of speakers and hearers, if we equate the semantic content of a sentence with its truth-conditions (.). So what should we do? Give up compositionality, or give up the assumption that what should be determined compositionality are the truth-conditions of a sentence? ” In fact, we will argue that neither of these assumptions has to be given up if we take a broader view on compositionality (Van Gelder’s 1990 functional compositionality) in addition to Blutner’s bidirectional optimization view on the relation between form and meaning. But before we explore this hypothesis, let us examine the question what is the current view on compositionality within Optimality Theory. Optimality Theory was developed in the 1990s by Alan Prince and Paul Smolensky as a general theory of language and grammar (cf. Prince & Smolensky, 1993, 1997). Optimality Theory applied to the domains of syntax and semantics involves two closely related issues: 1. given a semantic input, what is its optimal expression? , and 2. given a syntactic input, what is its optimal interpretation? In OT semantics, developed by Hendriks and de Hoop (1997, 2001), each grammatical expression is associated with an, in principle, infinite number of interpretations. These candidate interpretations are tested against the ranked constraints in a parallel fashion. One of the advantages of such an approach is that constraints of various nature (syntactic, pragmatic, etc.) interact with each other in a truly crossmodular way. This view crucially differs from the classical compositional approach, where interpretation is computed on the basis of the syntactic input, making use of context only when necessary. Whereas