A weak intuitionistic propositional logic with purely constructive implication
type: Item
instance of: scholarly article
title: A weak intuitionistic propositional logic with purely constructive implication
zbMATH Open document ID: 0644.03005
DOI: 10.1007/BF00370647
author: Mitsuhiro Okada
published in: Studia Logica
publication date: 1987-01-01T00:00:00Z
review text: By weakening the intuitionistic implication, two subsystems WLJ and SI of the sequent calculus LJ for intuitionistic logic are defined. The cut- elimination theorems for WLJ and SI are given and the corresponding constructive semantics is described. An interpretation of the system SI by means of modal operators and classical implication is considered, where a weak modal system WM is obtained. In the end of the paper, the Kripke models for WM are presented and the completeness theorem is proved.
Mathematics Subject Classification ID: 03B20
Mathematics Subject Classification ID: 03F05
Mathematics Subject Classification ID: 03B45
zbMATH DE Number: 4049612
zbMATH Keywords: sequent calculus
zbMATH Keywords: intuitionistic logic
zbMATH Keywords: cut-elimination
zbMATH Keywords: constructive semantics
zbMATH Keywords: modal operators
zbMATH Keywords: Kripke models
zbMATH Keywords: completeness
MaRDI profile type: Publication
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cites work: The consistency of arithmetics
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full work available at URL: https://doi.org/10.1007/bf00370647
OpenAlex ID: W2045641531
description: scientific article; zbMATH DE number 4049612