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 formalized 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.