Modal extensions of Lukasiewicz logic for modelling coalitional power

0471671 - ÚTIA 2018 RIV GB eng J - Journal Article
Kroupa, Tomáš - Teheux, B.
Modal extensions of Lukasiewicz logic for modelling coalitional power.
Journal of Logic and Computation. Roč. 27, č. 1 (2017), s. 129-154. ISSN 0955-792X. E-ISSN 1465-363X
R&D Projects: GA ČR GAP402/12/1309
Institutional support: RVO:67985556
Keywords : Coalition Logic * Lukasiewicz modal logic * effectivity function
OECD category: Pure mathematics
Impact factor: 0.740, year: 2017
http://library.utia.cas.cz/separaty/2017/MTR/kroupa-0471671.pdf

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.
Permanent Link: http://hdl.handle.net/11104/0271352