Logic and Computation Courses

Introductory Courses

Semantics based proof-search methods for non-classical logics

Camillo Fiorentini

Week 1, August 3-7, 2020

Abstract:

Proof theory for non-classical logics has been deeply investigated. Standard techniques to prove the completeness of a calculus are based on syntactic methods, mostly relying on cut-elimination. The main drawback is that, from a failed proof-search, no information about the non-validity of a formula is gained. An alternative way is to exploit semantics: to prove that a calculus is complete, one has to show that, whenever a formula is not provable in the calculus, a countermodel for it can be built.

A countermodel can be viewed as a certificate of the non-validity of a formula; moreover, from an inspection of the completeness proof, one can design efficient proof-search strategies for the calculus at hand. In the course we present efficient proof-search strategies supporting countermodel generation, focusing on Intuitionistic Propositional Logic. We present the main ideas beyond the technique and some significant examples.

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32nd European Summer School in Logic, Language and Information - ESSLLI 2021
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