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23 March 2021, The Utrecht Logic in Progress Series (TULIPS), Sebastian Melzer

Speaker: Sebastian Melzer (ILLC, Amsterdam)
Title: Canonical Formulas for the Lax Logic
Date: Tuesday 23 March 2021
Time: 16:00-17:15
Location: Online

Abstract: In this talk, we will investigate the method of canonical formulas for propositional lax logic. We construct “lax canonical formulas” using the local finiteness of the variety of nuclear implicative semilattices. These formulas provide a uniform axoimatization method for lax logics. Then we extend generalized Esakia duality to account for nuclear implicative semilattice homomorphisms between nuclear Heyting algebras, and explore the feasibility of lax analogues of subframe logics. This leads to the introduction of steady logics — logics characterized by generalized lax canonical formulas that only partially encode the modal structure of nuclear Heyting algebras. Finally, we use these generalized lax canonical formulas to obtain a number of preservation theorems, for example, we will prove that for each Kripke-complete intermediate logic the least lax logic containing it is also Kripke-complete.

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