0471671 20240103213702.520170228235959.9 85014645540 000397037900006 10.1093/logcom/exv081 Modal extensions of Lukasiewicz logic for modelling coalitional power 26 s. P cav_un_epca*02538590955-792XJournal of Logic and Computation271 (2017)129-154 Coalition Logic Lukasiewicz modal logic effectivity function cav_un_auth*0101141 Matematická teorie rozhodování Department of Decision Making Theory MTR MTR Department of Decision Making Theory 50 Kroupa Tomáš UTIA-B Ústav teorie informace a automatizace AV ČR, v. v. i. cav_un_auth*0306052 50 Teheux B. LU http://library.utia.cas.cz/separaty/2017/MTR/kroupa-0471671.pdf cav_un_auth*0284931 GAP402/12/1309 GA ČR 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. BA 10000 10100 10101 2018 2 RVO:67985556 http://hdl.handle.net/11104/0271352 S 3+4 Article Computer Science Theory Methods|Logic 3+4 Article Computer Science Theory Methods|Logic 3+4 Article Computer Science Theory Methods|Logic LOGIC|COMPUTERSCIENCE.THEORY&METHODS 0.710 0.505 8.2 0.00176 0.436 732 0.381 0.626 91 Q2 44.937 48.1 Q3 Q3 1.04 Q2 72.5 2017 85014645540 SCOPUS PUBMED 000397037900006 WOS cav_un_epca*0253859 Journal of Logic and Computation 0955-792X 1465-363X Roč. 27 č. 1 2017 129 154