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Oxford Quantum Talks Archive

Relational semantics in the not-necessarily-distributive setting

Mai Gehrke, Radboud University Nijmegen
Flowin'Cat 2010, October 2010, University of Oxford

Relational semantics for distributive and Boolean based logics are obtained from topological duals by forgetting the topology. Canonical extensions describe, in lattice theoretic terms, the relationship between the logic and the semantics thus obtained, and generalises in a straight forward manner to the not-necessarily-distributive setting. This canonical extension then, in turn, identifies for us what relational semantics in this setting should be and how to think about them. I'll give a brief overview of this relationship and some details on work with Anna Cherlinovskaya and Lorijn van Rooijen on semantics for Moortgat's Lambek-Grishin calculus with interaction axioms.

[video] [streaming video]