Competence in lexical semantics

We investigate from the competence standpoint two recent models of lexical semantics, algebraic conceptual representations and continuous vector models. Characterizing what it means for a speaker to be competent in lexical semantics remains perhaps the most significant stumbling block in reconciling the two main threads of semantics, Chomsky’s cognitivism and Montague’s formalism. As Partee (1979) already notes (see also Partee 2013), linguists assume that people know their language and that their brain is finite, while Montague assumed that words are characterized by intensions, formal objects that require an infinite amount of information to specify. In this paper we investigate two recent models of lexical semantics that rely exclusively on finite information objects: algebraic conceptual representations (ACR) (Wierzbicka, 1985; Kornai, 2010; Gordon et al., 2011), and continuous vector space (CVS) models which assign to each word a point in finitedimensional Euclidean space (Bengio et al., 2003; Turian et al., 2010; Pennington et al., 2014). After a brief introduction to the philosophical background of these and similar models, we address the hard questions of competence, starting with learnability in Section 2; the ability of finite networks or vectors to replicate traditional notions of lexical relatedness such as synonymy, antonymy, ambiguity, polysemy, etc. in Section 3; the interface to compositional semantics in Section 4; and language-specificity and universality in Section 5. Our survey of the literature is far from exhaustive: both ACR and CVS have deep roots, with significant precursors going back at least to Quillian (1968) and Osgood et al. (1975) respectively, but we put the emphasis on the computational experiments we ran (source code and lexica available at github.com/kornai/4lang).