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Logic programming: laxness and saturation

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If you have a question about this talk, please contact Tamara von Glehn.

(joint with Ekaterina Komendantskaya)

A propositional logic program P may be identified with a (Pf Pf)-coalgebra on the set of atomic propositions in the program. The corresponding C-coalgebra, where C is the cofree comonad on Pf Pf, describes derivations by resolution. That correspondence has been developed to model first-order programs in two ways, with lax semantics and saturated semantics, based on locally ordered categories and right Kan extensions respectively. We unify the two approaches, exhibiting them as complementary rather than competing, reflecting the theorem-proving and proof-search aspects of logic programming. While maintaining that unity, we further refine lax semantics to give finitary models of logic progams with existential variables, and to develop a precise semantic relationship between variables in logic programming and worlds in local state.

This talk is part of the Category Theory Seminar series.

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