The inverse method is a saturation based theorem proving technique; it relies on a forward proof-search strategy and can be applied to cut-free calculi enjoying the subformula property. This method has been successfully applied to a variety of logics. Here we apply this method to derive the unprovability of a goal formula G in Intuitionistic Propositional Logic. To this aim we design a forward calculus FRJ(G) for Intuitionistic unprovability. From a derivation of G in FRJ(G) we can extract a Kripke countermodel for G. Since in forward methods sequents are not duplicated, the generated countermodels do not contain redundant worlds and are in general very concise.

A forward unprovability calculus for intuitionistic propositional logic

Fiorentini, Camillo
;
Ferrari, Mauro
2017-01-01

Abstract

The inverse method is a saturation based theorem proving technique; it relies on a forward proof-search strategy and can be applied to cut-free calculi enjoying the subformula property. This method has been successfully applied to a variety of logics. Here we apply this method to derive the unprovability of a goal formula G in Intuitionistic Propositional Logic. To this aim we design a forward calculus FRJ(G) for Intuitionistic unprovability. From a derivation of G in FRJ(G) we can extract a Kripke countermodel for G. Since in forward methods sequents are not duplicated, the generated countermodels do not contain redundant worlds and are in general very concise.
2017
Fiorentini, Camillo*
Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
9783319669014
26th International Conference on Automated Reasoning with Analytic Tableaux and Related Methods, TABLEAUX 2017
bra
2017
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11383/2068070
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