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- Title
Restricted Rules of Inference and Paraconsistency.
- Authors
Basu, Sankha S; Chakraborty, Mihir K
- Abstract
In this paper, we study two companions of a logic, viz. the left variable inclusion companion and the restricted rules companion, their nature and interrelations, especially in connection with paraconsistency. A sufficient condition for the two companions to coincide has also been proved. Two new logical systems—intuitionistic paraconsistent weak Kleene logic (IPWK) and paraconsistent pre-rough logic (PPRL)—are presented here as examples of logics of left variable inclusion. IPWK is the left variable inclusion companion of intuitionistic propositional logic and is also the restricted rules companion of it. PPRL, on the other hand, is the left variable inclusion companion of pre-rough logic but differs from the restricted rules companion of it. We have discussed algebraic semantics for these logics in terms of Płonka sums. This amounts to introducing a contaminating truth value, intended to denote a state of indeterminacy.
- Subjects
PROPOSITION (Logic); ALGEBRAIC logic; SEMANTICS (Philosophy); LOGIC
- Publication
Logic Journal of the IGPL, 2022, Vol 30, Issue 3, p534
- ISSN
1367-0751
- Publication type
Article
- DOI
10.1093/jigpal/jzab019