A terminating sequent calculus for intuitionistic propositional logic is obtained by modifying the R superset of rule of the labelled sequent calculus G3I. This is done by adding a variant of the principle of a fortiori in the left-hand side of the premiss of the rule. In the resulting calculus, called G3I(t,) derivability of any given sequent is directly decidable by root-first proof search, without any extra device such as loop-checking. In the negative case, the failed proof search gives a finite countermodel to the sequent on a reflexive, transitive, and Noetherian Kripke frame. As a byproduct, a direct proof of faithfulness of the embedding of intuitionistic logic into Grzegorcyk logic is obtained.
A TERMINATING INTUITIONISTIC CALCULUS
FELLIN, GIULIO;NEGRI, SARA
2025-01-01
Abstract
A terminating sequent calculus for intuitionistic propositional logic is obtained by modifying the R superset of rule of the labelled sequent calculus G3I. This is done by adding a variant of the principle of a fortiori in the left-hand side of the premiss of the rule. In the resulting calculus, called G3I(t,) derivability of any given sequent is directly decidable by root-first proof search, without any extra device such as loop-checking. In the negative case, the failed proof search gives a finite countermodel to the sequent on a reflexive, transitive, and Noetherian Kripke frame. As a byproduct, a direct proof of faithfulness of the embedding of intuitionistic logic into Grzegorcyk logic is obtained.
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