Interactive Logic : Selected Papers from the 7th Augustus de Morgan Workshop, London
Johan van Benthem · Amsterdam University Press eBooks · 2008
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 multiagent, concurrent setting, including IF-style quantifiers.* This paper is an updated and reprinted version of "Socially Responsive, Environmentally Friendly Logic", published in [Ah 1 Pi 1 06, pp.17-45].