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First-order swap structures semantics for some Logics of Formal Inconsistency

Marcelo E. Coniglio, Aldo Figallo-Orellano & Ana Claudia Golzio

Journal of Logic and Computation 30 (6):1257-1290 (2020)

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Modal Logic With Non-Deterministic Semantics: Part II—Quantified Case.Marcelo E. Coniglio, Luis Fariñasdelcerro & Newton Marques Peron - 2022 - Logic Journal of the IGPL 30 (5):695-727.details In the first part of this paper we analyzed finite non-deterministic matrix semantics for propositional non-normal modal logics as an alternative to the standard Kripke possible world semantics. This kind of modal system characterized by finite non-deterministic matrices was originally proposed by Ju. Ivlev in the 70s. The aim of this second paper is to introduce a formal non-deterministic semantical framework for the quantified versions of some Ivlev-like non-normal modal logics. It will be shown that several well-known controversial issues of (...) Modal and Intensional Logic in Logic and Philosophy of Logic Direct download (3 more) Export citation Bookmark 1 citation
Twist-Valued Models for Three-Valued Paraconsistent Set Theory.Walter A. Carnielli & Marcelo E. Coniglio - forthcoming - Logic and Logical Philosophy:1.details We propose in this paper a family of algebraic models of ZFC based on the three-valued paraconsistent logic LPT0, a linguistic variant of da Costa and D’Ottaviano’s logic J3. The semantics is given by twist structures defined over complete Boolean agebras. The Boolean-valued models of ZFC are adapted to twist-valued models of an expansion of ZFC by adding a paraconsistent negation. This allows for inconsistent sets w satisfying ‘not (w = w)’, where ‘not’ stands for the paraconsistent negation. Finally, our (...) Logical Semantics and Logical Truth in Logic and Philosophy of Logic Many-Valued Logic in Logic and Philosophy of Logic Model Theory in Logic and Philosophy of Logic Set Theory in Philosophy of Mathematics Direct download (2 more) Export citation Bookmark 2 citations
Logics of Formal Inconsistency Enriched with Replacement: An Algebraic and Modal Account.Walter Carnielli, Marcelo E. Coniglio & David Fuenmayor - 2022 - Review of Symbolic Logic 15 (3):771-806.details One of the most expected properties of a logical system is that it can be algebraizable, in the sense that an algebraic counterpart of the deductive machinery could be found. Since the inception of da Costa's paraconsistent calculi, an algebraic equivalent for such systems have been searched. It is known that these systems are non self-extensional (i.e., they do not satisfy the replacement property). More than this, they are not algebraizable in the sense of Blok-Pigozzi. The same negative results hold (...) Logical Semantics and Logical Truth in Logic and Philosophy of Logic Mathematical Logic in Philosophy of Mathematics Modal Logic in Logic and Philosophy of Logic Paraconsistent Logic in Logic and Philosophy of Logic Semantics for Modal Logic in Logic and Philosophy of Logic Direct download (5 more) Export citation Bookmark 1 citation
Twist-Valued Models for Three-valued Paraconsistent Set Theory.Walter Carnielli & Marcelo E. Coniglio - 2021 - Logic and Logical Philosophy 30 (2):187-226.details Boolean-valued models of set theory were independently introduced by Scott, Solovay and Vopěnka in 1965, offering a natural and rich alternative for describing forcing. The original method was adapted by Takeuti, Titani, Kozawa and Ozawa to lattice-valued models of set theory. After this, Löwe and Tarafder proposed a class of algebras based on a certain kind of implication which satisfy several axioms of ZF. From this class, they found a specific 3-valued model called PS3 which satisfies all the axioms of (...) Paraconsistent Logic in Logic and Philosophy of Logic The Nature of Sets, Misc in Philosophy of Mathematics Direct download (2 more) Export citation Bookmark 2 citations

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