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  1. Modal Logic With Non-Deterministic Semantics: Part II—Quantified Case.Marcelo E. Coniglio, Luis Fariñasdelcerro & Newton Marques Peron - forthcoming - Logic Journal of the IGPL.
    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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  • 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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