Logic and Logical Philosophy 26 (2):197–206 (2017)
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| Abstract |
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 intermedi-
ate 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 sys-
tems 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.
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| Keywords | natural deduction regular logic Kleene’s logic three-valued logic |
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References found in this work BETA
On a Three-Valued Logical Calculus and its Application to the Analysis of the Paradoxes of the Classical Extended Functional Calculus.D. A. Bochvar & Merrie Bergmann - 1981 - History and Philosophy of Logic 2 (1-2):87-112.
Completeness Via Correspondence for Extensions of the Logic of Paradox.Barteld Kooi & Allard Tamminga - 2012 - Review of Symbolic Logic 5 (4):720-730.
View all 7 references / Add more references
Citations of this work BETA
An Epistemic Interpretation of Paraconsistent Weak Kleene Logic.Damian E. Szmuc - forthcoming - Logic and Logical Philosophy:1.
Note on 'Normalisation for Bilateral Classical Logic with Some Philosophical Remarks'.Nils Kürbis - 2021 - Journal of Applied Logics 7 (8):2259-2261.
Exactly True and Non-Falsity Logics Meeting Infectious Ones.Alex Belikov & Yaroslav Petrukhin - 2020 - Journal of Applied Non-Classical Logics 30 (2):93-122.
Generalized Correspondence Analysis for Three-Valued Logics.Yaroslav Petrukhin - 2018 - Logica Universalis 12 (3-4):423-460.
Unrestricted Quantification and Ranges of Significance.Thomas Schindler - forthcoming - Philosophical Studies:1-22.
View all 10 citations / Add more citations
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