Frege in Space: A Program for Composition Distributional Semantics

Frege in Space: A Program for Compositional Distributional Semantics Marco Baroni,1 Raffaella Bernardi1 and Roberto Zamparelli1 To Emanuele Pianta, in memoriam The lexicon of any natural language encodes a huge number of distinct word meanings. Just to understand this article, you will need to know what thousands of words mean. The space of possible sentential mean- ings is infinite: In this article alone, you will encounter many sentences that express ideas you have never heard before, we hope. Statistical semantics has addressed the issue of the vastness of word meaning by proposing methods to harvest meaning automatically from large collections of text (corpora). Formal semantics in the Fregean tradi- tion has developed methods to account for the infinity of sentential meaning based on the crucial insight of compositionality, the idea that meaning of sentences is built incrementally by combining the meanings of their constituents. This article sketches a new approach to seman- tics that brings together ideas from statistical and formal semantics to account, in parallel, for the richness of lexical meaning and the combinatorial power of sentential semantics. We adopt, in particular, the idea that word meaning can be approximated by the patterns of co-occurrence of words in corpora from statistical semantics, and the idea that compositionality can be captured in terms of a syntax-driven calculus of function application from formal semantics. 1Center for Mind/Brain Sciences and Department of Information Engineering and Computer Science, University of Trento (IT) 241 LiLT Volume 9 Perspectives on Semantic Representations for Textual Inference. Copyright c ⃝ 2014, CSLI Publications. 242 / Marco Baroni, Raffaella Bernardi and Roberto Zamparelli 1 Introduction Semantic compositionality is the crucial property of natural language according to which the meaning of a complex expression is a function of the meaning of its constituent parts and of the mode of their com- bination. Compositionality makes the meaning of a sentence such as “carnivorous plants digest slowly”, in (1), a function of the meaning of the noun phrase “carnivorous plants” combined as a subject with the meaning of the verb phrase “digest slowly”, which is in turn derived by the combination of the meaning of the verb digest and a modifier, the adverb slowly. (1) S VP Adv slowly VP V digest NP N plants Adj carnivorous Together with the property of syntactic recursivity, which grants humans the possibility of constructing indefinitely long grammatical sentences, semantic compositionality allows us to compose arbitrarily complex meanings into sentences, and extract meanings from arbitrarily long and complex sentences, starting from a finite lexicon. While the compositional nature of human language has been in some sense acknowledged since Aristotle’s subject-predicate distinction, it has been brought to the foreground only in modern times, mainly with the work of the German logician Gottlob Frege (hence the alternative name Frege’s Principle, see especially Frege 1892).2 Compositionality was later operationalized by Richard Montague (see in particular Mon- tague 1970b, 1973). Together with the assumption that meaning can be accounted for denotationally (that is in terms of whether a linguistic …

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