Natural Deduction systems for some subintuitionistic logics

Shirmohammadzadeh Maleki, Fatemeh

doi:10.30465/lsj.2024.49120.1472

Natural Deduction systems for some subintuitionistic logics

Document Type : Research

Author

Fatemeh Shirmohammadzadeh Maleki

Iranian Research Institute of Philosophy

https://doi.org/10.30465/lsj.2024.49120.1472

Abstract

Subintuitionistic logics as a theme were first studied by G. Corsi, who introduced a basic system F in a Hilbert style proof system. The system F is sound and complete with respect to the class of Kripke frames in which the assumption of preservation of truth is dropped and which are not assumed to be reflexive or transitive. Dick de Jongh and F. Sh. Maleki, have introduced a basic logic WF in a Hilbert style proof system, much weaker than F. They proved that subintuitionistic logic WF is sound and complete with respect to the class of neighborhood models with a somewhat more complex definition than the neighborhood models for classical (non-normal) modal logics. So far, no natural deduction system has been presented for any of these two basic systems F and WF. This paper is devoted to the introduction of natural deduction systems for subintuitionistic logics WF and F.

Keywords

Intuitionistic logic

Subintuitionistic logic F

Subintuitionistic logic WF

Natural deduction system

Hilbert style system

Subjects

Non-Standard Mathematical Logic

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