"Despite considerable successes in the last 40 years, formal semantics has not quite established itself as a field of great relevance to the broader enterprise of cognitive and social science. Besides the unavoidable technicality of formal semantic theories, there might be two substantive reasons. First, the lingua franca of cognitive science is the issue of the modular decomposition of the mind – but formal semantics has partly moved away from it: the sophisticated logical models of meaning in current use typically lump together all aspects of meaning in a big 'semantics-cum-pragmatics'. Second, formal semantics has remained somewhat parochial: it almost never crosses the frontiers of spoken language - despite the fact that questions of obvious interest arise in sign language; and it rarely addresses the relation between linguistic meaning and other cognitive systems, be it in humans or in related species. While strictly adhering to the formal methodology of contemporary semantics, we will seek to expand the frontiers of the field, with one leading question: what is the modular organization of meaning?
(i) First, we will help establish a new subfield of sign language formal semantics, with an initial focus on anaphora; we will ask whether the interaction between an abstract anaphoric module and the special geometric properties of sign language can account for the similarities and differences between sign and spoken language pronouns.
(ii) Second, we will revisit issues of modular decomposition between semantics and pragmatics by trying to disentangle modules that have been lumped together in recent semantic theorizing, in particular in the domains of presupposition, anaphora and conventional implicatures.
(iii) Third, we will ask whether some semantic modules might have analogues in other cognitive systems by investigating (a) possible precursors of semantics in primate vocalizations, and (b) possible applications of focus in music."
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