Reasoning about graded modalities in strategy logic

Strategy Logic is a powerful formalism useful to describe game concepts in multi-agent settings by explicitly quantifying over strategies treated as first-order citizens. In this talk we introduce Graded Strategy Logic (GSL), an extension of Strategy Logic along with graded quantifiers. This allows us to express properties such as “there are at least g strategies" satisfying a given objective. As different strategies may induce the same outcome, although looking different, the main difficulty in defining GSL is the design of a valid machinery to count strategies, as we show. To give an evidence of GSL usability, we investigate basic questions over this logic. In particular, we report on positive results about the determinacy of turn-based games and the related model-checking problem over a restricted fragment of this logic, which we show to be PTime-Complete. This talk is based of a paper autored by: Vadim Malvone, Fabio Mogavero, Aniello Murano and Loredana Sorrentino

Authors

• Vadim Malvone Télécom Paris

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