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For each n ∈ N , we introduce the algebraic semantics for the minimum many-valued modal logic over the MV-chain with n elements. We prove that this quasivariety of algebras is generated by the complex algebras, obtaining as a consequence the completeness result of the logic with respect to the Kripke semantics. As a first step towards the study of this algebraic semantics, we study some congruences of the complex algebras. [ABSTRACT FROM AUTHOR]

The present paper establishes systematic connections among the first-order correspondents of Sahlqvist modal reduction principles in various relational semantic settings, including crisp and many-valued Kripke frames, and crisp and many-valued polarity-based frames (aka enriched formal contexts). Building on unified correspondence theory, we aim at introducing a theoretical environment which makes it possible to: (a) compare and inter-relate the various frame correspondents (in different relational settings) of any given Sahlqvist modal reduction principle; (b) recognize when first-order sentences in the frame-correspondence languages of different types of relational structures encode the same "modal content"; (c) meaningfully transfer and represent well known relational properties such as reflexivity, transitivity, symmetry, seriality, confluence, density, across different semantic contexts. These results can be understood as a first step in a research program aimed at making correspondence theory not just (methodologically) unified, but also (effectively) parametric. [ABSTRACT FROM AUTHOR]

This paper continues the investigation of the logic of competing theories (be they scientific, social, political etc.) initiated in [4]. We introduce a many-valued, multi-type modal language which we endow with relational semantics based on enriched reflexive graphs, inspired by Ploščica's representation of general lattices. We axiomatize the resulting many-valued, non-distributive modal logic of these structures and prove a completeness theorem. We illustrate the application of this logic through a case study in which we model competition among interacting political promises and social demands within an arena of political parties social groups. [ABSTRACT FROM AUTHOR]

We introduce fuzzy relational modalities of necessity and possibility designed to handle propositions that can be truth-valueless. We identify several important types of these modalities, corresponding to families of connectives and quantifiers of fuzzy partial logic (Bochvar, Sobociński, Kleene) and show some of their properties. We also present a faithful syntactic translation of the resulting fuzzy partial modal logic to first-order fuzzy partial logic. [ABSTRACT FROM AUTHOR]

The majority of works on modal many-valued logics consider Kripke-style possible worlds frames as the principal semantics despite their well-known axiomatizability issues when considering non-Boolean accessibility relations. The present work explores a more general semantical picture, namely a many-valued version of the classical neighborhood semantics. We present it in two levels of generality. First, we work with modal languages containing only the two usual unary modalities, define neighborhood frames over algebras of the logic FL ew with operators, and show their relation with the usual Kripke semantics (this is actually the highest level of generality where one can give a straightforward definition of the Kripke-style semantics). Second, we define generalized neighborhood frames for arbitrary modal languages over a given class of algebras for an arbitrary protoalgebraic logic and, assuming certain additional conditions, axiomatize the logic of all such frames (which generalizes the completeness theorem of the classical modal logic E with respect to classical neighborhood frames). [ABSTRACT FROM AUTHOR]