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Summary: A Compositional Game Semantics for Multi-Agent Logics of
Partial Information
Samson Abramsky
Oxford University Computing Laboratory
Abstract
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.
Contents
1 Introduction 2
2 From 2-person to n-person games 3
2.1 The naturalness of 2-person games . . . . . . . . . . . . . . . . . . . . . . . . 3
2.2 Background: 2-person games . . . . . . . . . . . . . . . . . . . . . . . . . . . 3
2.3 An Aside . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4
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