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The most representative interval temporal logic, called HS, was introduced by Halpern and Shoham in the nineties. Recently, HS has been proposed as a suitable formalism for modern artificial intelligence applications; however, when dealing with real-life data one is not always able to express temporal relations and propositional labels in a definite, crisp way. In this paper, following the seminal ideas of Fitting and Zadeh, we present a fuzzy generalization of HS, called FHS, that partially solves such problems of expressive power. We study FHS from both a theoretical and an application standpoint: first, we discuss its syntax, semantics, expressive power, and satisfiability problem; then, we define and solve the time series FHS finite model checking problem, to serve as the basis of future applications. [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]