We develop a vector space semantics for verb phrase ellipsis with anaphora using type-driven compositional distributional semantics based on the Lambek calculus with limited contraction of Jäger. Distributional semantics has a lot to say about the statistical collocation based meanings of content words, but provides little guidance on how to treat function words. Formal semantics on the other hand, has powerful mechanisms for dealing with relative pronouns, coordinators, and the like. Type-driven compositional distributional semantics brings these two models together. We (...) review previous compositional distributional models of relative pronouns, coordination and a restricted account of ellipsis in the DisCoCat framework of Coecke et al. :1079–1100, 2013). We show how DisCoCat cannot deal with general forms of ellipsis, which rely on copying of information, and develop a novel way of connecting typelogical grammar to distributional semantics by assigning vector interpretable lambda terms to derivations of LCC in the style of Muskens and Sadrzadeh Logical aspects of computational linguistics, Springer, Berlin, 2016). What follows is an account of ellipsis in which word meanings can be copied: the meaning of a sentence is now a program with non-linear access to individual word embeddings. We present the theoretical setting, work out examples, and demonstrate our results with a state of the art distributional model on an extended verb disambiguation dataset. (shrink)

This is the first part of a two-part article on semantic compositionality, that is, the principle that the meaning of a complex expression is determined by the meanings of its parts and the way they are put together. Here we provide a brief historical background, a formal framework for syntax and semantics, precise definitions, and a survey of variants of compositionality. Stronger and weaker forms are distinguished, as well as generalized forms that cover extra-linguistic context dependence as well as linguistic (...) context dependence. In the second article, we survey arguments for and arguments against the claim that natural languages are compositional, and consider some problem cases. It will be referred to as Part II. (shrink)

This paper starts from the observation that the standard arguments for compositionality are really arguments for the computability of semantics. Since computability does not entail compositionality, the question of what justifies compositionality recurs. The paper then elaborates on the idea of recursive semantics as corresponding to computable semantics. It is then shown by means of time complexity theory and with the use of term rewriting as systems of semantic computation, that syntactically unrestricted, noncompositional recursive semantics leads to computational explosion (factorial (...) complexity). Hence, with combinatorially unrestricted syntax, semantics with tractable time complexity is compositional. (shrink)

A semantics may be compositional and yet partial, in the sense that not all well-formed expressions are assigned meanings by it. Examples come from both natural and formal languages. When can such a semantics be extended to a total one, preserving compositionality? This sort of extension problem was formulated by Hodges, and solved there in a particular case, in which the total extension respects a precise version of the fregean dictum that the meaning of an expression is the contribution it (...) makes to the meanings of complex phrases of which it is a part. Hodges' result presupposes the so-called Husserl property, which says roughly that synonymous expressions must have the same category. Here I solve a different version of the compositional extension problem, corresponding to another type of linguistic situation in which we only have a partial semantics, and without assuming the Husserl property. I also briefly compare Hodges' framework for grammars in terms of partial algebras with more familiar ones, going back to Montague, which use many-sorted algebras instead. (shrink)

Ordinary semantic compositionality (meaning of whole determined from meanings of parts plus composition) can serve to explain how a hearer manages to assign an appropriate meaning to a new sentence. But it does not serve to explain how the speaker manages to find an appropriate sentence for expressing a new thought. For this we would need a principle of inverse compositionality, by which the expression of a complex content is determined by the expressions of it parts and the mode of (...) composition. But this presupposes that contents have constituent structure, and this cannot be taken for granted. However, it can be proved that if a certain principle of substitutivity is valid for a particular language, then the meanings expressed by its sentences can justifiably be treated as structured. In its simplest form, this principle says that if in a complex expression a constituent is replaced by another constituent with a different meaning, the new complex has a meaning different from the original. This principle is again inversely related to the normal compositional principle of substitutivity. The combination of ordinary and inverse compositionality is here called 'strong compositionality'. The proof is carried out in the algebraic framework developed by Wilfrid Hodges and Dag Westerståhl. (shrink)

Is there a reason to believe that the evolution of language leads to compositional semantics? A proposal from Henry Brighton is presented and criticized. As an alternative, the role of compositionality for the complexity of semantic interpretation is emphasized.

This dissertation is a contribution to the philosophy of language. Its central question is: In virtue of which facts do linguistic expressions mean what they do? E.g. why does “apple” mean apple in English? The question receives a systematic answer; in short: Linguistic expressions mean what they do because among their users, there are linguistic conventions and social norms to use and understand them in certain ways. The answer is clarified and defended as a central thesis. For in this form, (...) it is at best a slogan: What is meaning? What is it to use and understand expressions? What are conventions and social norms anyway? How does the use and understanding determine meaning? The goal of the dissertation consists in answering these questions. (shrink)