A weak intuitionistic propositional logic with purely constructive implication

Mitsuhiro Okada

doi:10.1007/BF00370647

A weak intuitionistic propositional logic with purely constructive implication

Mitsuhiro Okada

Research output: Contribution to journal › Article › peer-review

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Abstract

We introduce subsystems WLJ and SI of the intuitionistic propositional logic LJ, by weakening the intuitionistic implication. These systems are justifiable by purely constructive semantics. Then the intuitionistic implication with full strength is definable in the second order versions of these systems. We give a relationship between SI and a weak modal system WM. In Appendix the Kripke-type model theory for WM is given.

Original language	English
Pages (from-to)	371-382
Number of pages	12
Journal	Studia Logica
Volume	46
Issue number	4
DOIs	https://doi.org/10.1007/BF00370647
Publication status	Published - 1987 Dec 1
Externally published	Yes

ASJC Scopus subject areas

Logic
History and Philosophy of Science

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10.1007/BF00370647

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title = "A weak intuitionistic propositional logic with purely constructive implication",

abstract = "We introduce subsystems WLJ and SI of the intuitionistic propositional logic LJ, by weakening the intuitionistic implication. These systems are justifiable by purely constructive semantics. Then the intuitionistic implication with full strength is definable in the second order versions of these systems. We give a relationship between SI and a weak modal system WM. In Appendix the Kripke-type model theory for WM is given.",

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AB - We introduce subsystems WLJ and SI of the intuitionistic propositional logic LJ, by weakening the intuitionistic implication. These systems are justifiable by purely constructive semantics. Then the intuitionistic implication with full strength is definable in the second order versions of these systems. We give a relationship between SI and a weak modal system WM. In Appendix the Kripke-type model theory for WM is given.

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A weak intuitionistic propositional logic with purely constructive implication

Abstract

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