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  1. Two Decision Procedures for da Costa’s $$C_n$$ C n Logics Based on Restricted Nmatrix Semantics.Marcelo E. Coniglio & Guilherme V. Toledo - 2022 - Studia Logica 110 (3):601-642.
    Despite being fairly powerful, finite non-deterministic matrices are unable to characterize some logics of formal inconsistency, such as those found between mbCcl and Cila. In order to overcome this limitation, we propose here restricted non-deterministic matrices (in short, RNmatrices), which are non-deterministic algebras together with a subset of the set of valuations. This allows us to characterize not only mbCcl and Cila (which is equivalent, up to language, to da Costa's logic C_1) but the whole hierarchy of da Costa's calculi (...)
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  • Modal logic with non-deterministic semantics: Part I—Propositional case.Marcelo E. Coniglio, Fariñas Del Cerro Luis & Marques Peron Newton - 2020 - Logic Journal of the IGPL 28 (3):281-315.
    Dugundji proved in 1940 that most parts of standard modal systems cannot be characterized by a single finite deterministic matrix. In the eighties, Ivlev proposed a semantics of four-valued non-deterministic matrices, in order to characterize a hierarchy of weak modal logics without the necessitation rule. In a previous paper, we extended some systems of Ivlev’s hierarchy, also proposing weaker six-valued systems in which the axiom was replaced by the deontic axiom. In this paper, we propose even weaker systems, by eliminating (...)
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  • Combining Swap Structures: The Case of Paradefinite Ivlev-Like Modal Logics Based on $$FDE$$.Marcelo E. Coniglio - forthcoming - Studia Logica:1-52.
    The aim of this paper is to combine several Ivlev-like modal systems characterized by 4-valued non-deterministic matrices (Nmatrices) with $$\mathcal {IDM}4$$, a 4-valued expansion of Belnap–Dunn’s logic $$FDE$$ with an implication introduced by Pynko in 1999. In order to do this, we introduce a new methodology for combining logics which are characterized by means of swap structures, based on what we call superposition of snapshots. In particular, the combination of $$\mathcal {IDM}4$$ with $$Tm$$, the 4-valued Ivlev’s version of KT, will (...)
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  • Ivlev-Like Modal Logics of Formal Inconsistency Obtained by Fibring Swap Structures.Marcelo E. Coniglio - forthcoming - Studia Logica:1-70.
    The aim of this paper is to give the first steps towards the formal study of swap structures, which are non-deterministic matrices (Nmatrices) defined over tuples of 0–1 truth values generalizing the notion of twist structures. To do this, a precise notion of clauses which axiomatize bivaluation semantics is proposed. From this specification, a swap structure is naturally induced. This formalization allows to define the combination by fibring of two given logics described by swap structures generated by clauses in a (...)
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  • 8 Valued Non-Deterministic Semantics for Modal Logics.Pawel Pawlowski & Daniel Skurt - 2024 - Journal of Philosophical Logic 53 (2):351-371.
    The aim of this paper is to study a particular family of non-deterministic semantics for modal logics that has eight truth-values. These eight-valued semantics can be traced back to Omori and Skurt (2016), where a particular member of this family was used to characterize the normal modal logic K. The truth-values in these semantics convey information about a proposition’s truth/falsity, whether the proposition is necessary/not necessary, and whether it is possible/not possible. Each of these triples is represented by a unique (...)
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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.
    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 (...)
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  • Many-valued logic of informal provability: A non-deterministic strategy.Pawel Pawlowski & Rafal Urbaniak - 2018 - Review of Symbolic Logic 11 (2):207-223.
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  • Errata and Addenda to ‘Finite non-deterministic semantics for some modal systems’.Marcelo E. Coniglio, Luis Fariñas del Cerro & Newton M. Peron - 2016 - Journal of Applied Non-Classical Logics 26 (4):336-345.
    In this note, an error in the axiomatization of Ivlev’s modal system Sa+ which we inadvertedly reproduced in our paper “Finite non-deterministic semantics for some modal systems”, is fixed. Additionally, some axioms proposed in were slightly modified. All the technical results in which depend on the previous axiomatization were also fixed. Finally, the discussion about decidability of the level valuation semantics initiated in is taken up. The error in Ivlev’s axiomatization was originally pointed out by H. Omori and D. Skurt (...)
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  • Society semantics and the logic way to collective intelligence.Walter Carnielli & Mamede Lima-Marques - 2017 - Journal of Applied Non-Classical Logics 27 (3-4):255-268.
    The so-called phenomenon of collective intelligence is now a burgeoning movement, with several guises and examples in many areas. We briefly survey some relevant aspects of collective intelligence in several formats, such as social software, crowdfunding and convergence, and show that a formal version of this paradigm can also be posed to logic systems, by employing the notion of logic societies. The paradigm of logical societies has lead to a new notion of distributed semantics, the society semantics, with theoretical advances (...)
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