Categorial Grammar at a Cross-Roads

Categorial grammars are driven by resource logics in a proof format Benthem, 1991; Mootrgat, 1997). Thus, they revolve around derivation and computation, with theCurry-Howard. 1997 Gestalt switch taking proofs to type-theoretic denotions for the expression analyzed. But over thye past decades, categorial logics have also been analyzed model-theoretically in modal logics with standard possible worlds-style models (cf. Kurtonina, 1995). Then, e.g., a categorial product A•B ‘true ‚ of some objects, t, u satisfying A,B, respectively. This is a standard binary modality, which needs a ternary accessibility relation R for its abstract truth condition: M,8⊨ A•B iff ∃t, υ: Rs, tu & M,t ⊨ A & M,u ⊨ B Modal logic is a world of research rather different from the usual concerns in categorial grammar. What happens when we put the two agendas side by side?

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