Socially Responsive, Environmentally Friendly Logic

We consider the following questions: What kind of logic has a natural semantics in multi-player (rather than 2-player) games? How can we express branching quantifiers, and other partial-information constructs, with a properly compositional syntax and semantics? We develop a logic in answer to these questions, with a formal semantics based on multiple concurrent strategies, formalized as closure operators on Kahn-Plotkin concrete domains. Partial information constraints are represented as co-closure operators. We address the syntactic issues by treating syntactic constituents, including quantifiers, as arrows in a category, with arities and co-arities. This enables a fully compositional account of a wide range of features in a multi-agent, concurrent setting, including IF-style quantifiers.