Natural Deduction for Three-Valued Regular Logics

• Authors: Petrukhin Yaroslav
• Languages of publication: EN

Abstracts

EN

In this paper, I consider a family of three-valued regular logics: the well-known strong and weak S.C. Kleene’s logics and two intermediate logics, where one was discovered by M. Fitting and the other one by E. Komendantskaya. All these systems were originally presented in the semantical way and based on the theory of recursion. However, the proof theory of them still is not fully developed. Thus, natural deduction systems are built only for strong Kleene’s logic both with one (A. Urquhart, G. Priest, A. Tamminga) and two designated values (G. Priest, B. Kooi, A. Tamminga). The purpose of this paper is to provide natural deduction systems for weak and intermediate regular logics both with one and two designated values.

Keywords

EN

natural deduction; regular logic; Kleene’s logic; three-valued logic

• Publisher: Uniwersytet Mikołaja Kopernika (Nicolaus Copernicus University in Toruń)
• Journal: Logic and Logical Philosophy
• Year: 2017
• Volume: 26
• Issue: 2
• Pages: 197–206

Dates

published

2017-06-15

Contributors

author

Petrukhin Yaroslav

• Department of Philosophy, Moscow State University, Moscow, Russia

References

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Identifiers

DOI

10.12775/LLP.2016.025