Paraconsistent logic

About: Paraconsistent logic is a research topic. Over the lifetime, 1610 publications have been published within this topic receiving 28842 citations.

Making Sense of Paraconsistent Logic: The Nature of Logic, Classical Logic and Paraconsistent Logic

Abstract: Max Cresswell and Hilary Putnam seem to hold the view, often shared by classical logicians, that paraconsistent logic has not been made sense of, despite its well-developed mathematics. In this paper, I examine the nature of logic in order to understand what it means to make sense of logic. I then show that, just as one can make sense of non-normal modal logics (as Cresswell demonstrates), we can make ‘sense’ of paraconsistent logic. Finally, I turn the tables on classical logicians and ask what sense can be made of explosive reasoning. While I acknowledge a bias on this issue, it is not clear that even classical logicians can answer this question.

Tableaux with Four Signs as a Unified Framework

Abstract: We show that the use of tableaux with four types of signed formulas (the signs intuitively corresponding to positive/negative information concerning truth/falsity) provides a framework in which a diversity of logics can be handled in a uniform way. The logics for which we provide sound and complete tableau systems of this type are classical logic, the most important three-valued logics, the four-valued logic of logical bilattices (an extension of Belnap’s four-valued logic), Nelson’s logics for constructive negation, and da Costa’s paraconsistent logic C ω (together with some of its extensions). For the latter we provide new, simple semantics for which our tableau systems are sound and complete.

On the strongest three-valued paraconsistent logic contained in classical logic and its dual

Abstract: LP⊃,F is a three-valued paraconsistent propositional logic that is essentially the same as J3. It has the most properties that have been proposed as desirable properties of a reasonable paraconsistent propositional logic. However, it follows easily from already published results that there are exactly 8192 different three-valued paraconsistent propositional logics that have the properties concerned. In this paper, properties concerning the logical equivalence relation of a logic are used to distinguish LP⊃,F from the others. As one of the bonuses of focusing on the logical equivalence relation, it is found that only 32 of the 8192 logics have a logical equivalence relation that satisfies the identity, annihilation, idempotent and commutative laws for conjunction and disjunction. For most properties of LP⊃,F that have been proposed as desirable properties of a reasonable paraconsistent propositional logic, its paracomplete analogue has a comparable property. In this paper, properties concerning the logical equivalence relation of a logic are also used to distinguish the paracomplete analogue of LP⊃,F from the other three-valued paracomplete propositional logics with those comparable properties.

New Waves in Philosophical Logic

Abstract: Series Editors' Preface Acknowledgements Notes on Contributors How Things Are Elsewhere W. Schwarz Information Change and First-Order Dynamic Logic B.Kooi Interpreting and Applying Proof Theories for Modal Logic F.Poggiolesi & G.Restall The Logic(s) of Modal Knowledge D.Cohnitz On Probabilistically Closed Languages H.Leitgeb Dogmatism, Probability and Logical Uncertainty B.Weatherson & D.Jehle Skepticism about Reasoning S.Roush, K.Allen & I.Herbert Lessons in Philosophy of Logic from Medieval Obligations C.D.Novaes How to Rule Out Things with Words: Strong Paraconsistency and the Algebra of Exclusion F.Berto Lessons from the Logic of Demonstratives G.Russell The Multitude View on Logic M.Eklund Index