GLOWS · Game Logic of Weighted Strategies

Game logic is a well-known formalism to model strategic ability in two-player games, allowing one to reason about program correctness in distributed settings where the environment is viewed as an 'opponent'. For example, this has been successfully applied to hybrid systems and neural networks. The project GLOWS initiates the study of weighted game logics, which are capable of describing strategic ability in two-player games which involve quantitative data. For instance, this allows one to model games with graded payoffs (e.g., players can win different amounts) and games with probabilistic elements (e.g., outcomes being decided by the roll of a dice). To model this quantitative data, strategies and outcomes are weighted in a quantale. Within GLOWS, quantale-weighted game constructs and their logics will be introduced and motivated by presenting their potential applications in theoretical computer science and beyond. It will be shown that these logics embed into quantale-valued modal mu-calculi, and this will be exploited in order to prove their decidability. Furthermore, it will be proved that game constructs are safe under bisimilarity and non-expansive under behavioural distance. Lastly, sound and complete axiomatizations of weighted game logics are provided. To achieve these results, powerful mathematical toolkits such as coalgebraic logic and quantale-enriched category theory will be exploited, showcasing the importance and applicability of mathematics in theoretical computer science and giving the project an interdisciplinary character. In this context, the project GLOWS is highly relevant, as it addresses a current major challenge in computer science - devising logical systems capable of appropriately handling quantitative data.