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- Title
NATURAL DEDUCTION FOR THREE-VALUED REGULAR LOGICS.
- Authors
Petrukhin, Yaroslav
- 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 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.
- Subjects
NATURAL deduction (Logic); TERNARY logic; SEMANTICS; KLEENE algebra; RECURSION theory
- Publication
Logic & Logical Philosophy, 2017, Vol 26, Issue 2, p197
- ISSN
1425-3305
- Publication type
Article
- DOI
10.12775/LLP.2016.025