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ArticleOriginal scientific text

Title

From Intuitionism to Brouwer's Modal Logic

Authors 1

Affiliations

  1. Opole University of Technology

Abstract

We try to translate the intuitionistic propositional logic INT into Brouwer's modal logic KTB. Our translation is motivated by intuitions behind Brouwer's axiom p →☐◊p The main idea is to interpret intuitionistic implication as modal strict implication, whereas variables and other positive sentences remain as they are. The proposed translation preserves fragments of the Rieger-Nishimura lattice which is the Lindenbaum algebra of monadic formulas in INT. Unfortunately, INT is not embedded by this mapping into KTB.

Keywords

ENG
intuitionistic logic, Kripke frames, Brouwer's modal logic

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Bulletin of the Section of Logic
2020/49/4
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Pages:
343-358
Main language of publication
English
Published
2020-12-30
Published online
2020-12-30

DOI: 10.18778/0138-0680.2020.22

Exact and natural sciences