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Modal extensions of Lukasiewicz logic for modelling coalitional power
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SYSNO ASEP 0471671 Document Type J - Journal Article R&D Document Type Journal Article Subsidiary J Článek ve WOS Title Modal extensions of Lukasiewicz logic for modelling coalitional power Author(s) Kroupa, Tomáš (UTIA-B) RID
Teheux, B. (LU)Number of authors 2 Source Title Journal of Logic and Computation - ISSN 0955-792X
Roč. 27, č. 1 (2017), s. 129-154Number of pages 26 s. Publication form Print - P Language eng - English Country GB - United Kingdom Keywords Coalition Logic ; Lukasiewicz modal logic ; effectivity function Subject RIV BA - General Mathematics OECD category Pure mathematics R&D Projects GAP402/12/1309 GA ČR - Czech Science Foundation (CSF) Institutional support UTIA-B - RVO:67985556 UT WOS 000397037900006 EID SCOPUS 85014645540 DOI https://doi.org/10.1093/logcom/exv081 Annotation Modal logics for reasoning about the power of coalitions capture the notion of effectivity functions associated with game forms. The main goal of coalition logics is to provide formal tools for modelling the dynamics of a game frame whose states may correspond to different game forms. The two classes of effectivity functions studied are the families of playable and truly playable effectivity functions, respectively. In this article, we generalize the concept of effectivity function beyond the yes/no truth scale. This enables us to describe the situations in which the coalitions assess their effectivity in degrees, based on functions over the outcomes taking values in a finite Lukasiewicz chain. Then we introduce two modal extensions of Lukasiewicz finite-valued logic together with many-valued neighbourhood semantics in order to encode the properties of many-valued effectivity functions associated with game forms. As our main results we prove completeness theorems for the two newly introduced modal logics. Workplace Institute of Information Theory and Automation Contact Markéta Votavová, votavova@utia.cas.cz, Tel.: 266 052 201. Year of Publishing 2018
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