A categorial type logic

In logical categorial grammar [23,11] syntactic structures are categorial proofs and semantic structures are intuitionistic proofs, and the syntax-semantics interface comprises a homomorphism from syntactic proofs to semantic proofs. Thereby, logical categorial grammar embodies in a pure logical form the principles of compositionality, lex-icalism, and parsing as deduction. Interest has focused on multimodal versions but the advent of the (dis)placement calculus of Morrill, Valentín and Fadda [21] suggests that the role of structural rules can be reduced, and this facilitates computational implementation. In this paper we specify a comprehensive formalism of (dis) placement logic for the parser/theorem prover CatLog integrating categorial logic connectives proposed to date and illustrate with a cover grammar of the Montague fragment