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Oxford Quantum Talks Archive

Beyond the context-free boundary: generalizing Lambek calculus

Michael Moortgat, University of Utrecht
Flowin'Cat 2010, October 2010, University of Oxford

The syntactic calculus, as proposed by Lambek in 1961, is a logic without structural rules: rules affecting multiplicity (contraction, weakening) or structure (commutativity, associativity) of the grammatical resources are not considered. In terms of expressivity, this calculus is strictly context-free, a property shared by the associative calculus of (Lambek 1958) and its simplified pregroup version. The context-free limitation makes itself felt in situations where syntactic and semantic composition seem to be out of sync. In the talk, I discuss the Lambek-Grishin calculus, a symmetric generalization of the syntactic calculus taking its inspiration from Grishin (1983). I focus on two features that help resolve tensions at the syntax-semantics interface: -A continuation-passing-style interpretation, making contexts an explicit part of the composition process. As a result of the richer view on the mapping between syntax and semantics, the syntactic source calculus itself can be kept very simple. Distributivity principles relating Lambek's original type-forming operations and their duals. These principles characterize syntactic deformations under which interpretations are stable.

[video] [streaming video] [slides]