Intuitionistic Propositional Calculus in the Extended Framework with Modal Operator. Part II

Inoué, Takao; Hanaoka, Riku

doi:10.2478/forma-2022-0001

Abstract

This paper is a continuation of Inoué [5]. As already mentioned in the paper, a number of intuitionistic provable formulas are given with a Hilbert-style proof. For that, we make use of a family of intuitionistic deduction theorems, which are also presented in this paper by means of Mizar system [2], [1]. Our axiom system of intuitionistic propositional logic IPC is based on the propositional subsystem of H₁-IQC in Troelstra and van Dalen [6, p. 68]. We also owe Heyting [4] and van Dalen [7]. Our treatment of a set-theoretic intuitionistic deduction theorem is due to Agata Darmochwał’s Mizar article “Calculus of Quantifiers. Deduction Theorem” [3].

References

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Intuitionistic Propositional Calculus in the Extended Framework with Modal Operator. Part II

Abstract

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