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Synthese

, Volume 165, Issue 2, pp 269–294 | Cite as

Quantified coalition logic

  • Thomas Ågotnes
  • Wiebe van der Hoek
  • Michael Wooldridge
Article

Abstract

We add a limited but useful form of quantification to Coalition Logic, a popular formalism for reasoning about cooperation in game-like multi-agent systems. The basic constructs of Quantified Coalition Logic (QCL) allow us to express such properties as “every coalition satisfying property P can achieve φ” and “there exists a coalition C satisfying property P such that C can achieve φ”. We give an axiomatisation of QCL, and show that while it is no more expressive than Coalition Logic, it is nevertheless exponentially more succinct. The complexity of QCL model checking for symbolic and explicit state representations is shown to be no worse than that of Coalition Logic, and satisfiability for QCL is shown to be no worse than satisfiability for Coalition Logic. We illustrate the formalism by showing how to succinctly specify such social choice mechanisms as majority voting, which in Coalition Logic require specifications that are exponentially long in the number of agents.

Keywords

Coalition logic Quantification Succinctness Model checking Satisfiability 

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Copyright information

© Springer Science+Business Media B.V. 2008

Authors and Affiliations

  • Thomas Ågotnes
    • 1
  • Wiebe van der Hoek
    • 2
  • Michael Wooldridge
    • 2
  1. 1.Department of Computer EngineeringBergen University CollegeBergenNorway
  2. 2.Department of Computer ScienceUniversity of LiverpoolLiverpoolEngland, UK

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