Title: Graded modal logic to reason about the power of attributes in multicriteria decision making.

In strategic games, the power of coalitions of players can be measured through the effectivity function of the game. This function aims to model the power distribution of the game among individuals and groups of individuals. 

In the talk, we first illustrate the limitation of this approach in contexts in which graded information is meaningful, as in Multi Criteria Decision Making for instance. 

From this observation, we define many-valued effectivity functions which aim to capture the degree with which a group of players can enforce a set (or a fuzzy set) of outcome states. 

We use a modal extension of the language of Łukasiewicz many-valued logic to capture the properties of these functions into deductive systems that allow to reason about many-valued effectivity. We also provide a many-valued neighborhood semantic as well as a completeness result for the smallest of these systems. This talk is based on joint research with Tomáš Kroupa from the Institute of Information Theory and Automation of the ASCR, Czech Republic.