On the logic of cooperation and propositional control

Cooperation logics have recently begun to attract attention within the multi-agent systems community. Using a cooperation logic, it is possible to represent and reason about the strategic powers of agents and coalitions of agents in game-like multi-agent systems. These powers are generally assumed to be implicitly defined within the structure of the environment, and their origin is rarely discussed. In this paper, we study a cooperation logic in which agents are each assumed to control a set of propositional variables--the powers of agents and coalitions then derive from the allocation of propositions to agents. The basic modal constructs in this Coalition Logic of Propositional Control (CL-PC) allow us to express the fact that a group of agents can cooperate to bring about a certain state of affairs. After motivating and introducing CL-PC, we provide a complete axiom system for the logic, investigate the issue of characterising control in CL-PC with respect to the underlying power structures of the logic, and formally investigate the relationship between CL-PC and Pauly's Coalition Logic. We then show that the model checking and satisfiability problems for CL-PC are both PSPACE-complete, and conclude by discussing our results and how CL-PC sits in relation to other logics of cooperation.

[1]  Joseph Y. Halpern.  Proceedings of the 1986 Conference on Theoretical aspects of reasoning about knowledge , 1986 .

[2]  M. Pauly.  A Logical Framework for Coalitional Effectivity in Dynamic Procedures , 2001 .

[3]  N. Belnap.  Backwards and Forwards in the Modal Logic of Agency , 1991 .

[4]  D. Fensel.  Principles of knowledge representation and reasoning : proceedings of the eighth International Conference (KR2002), Toulouse, France, April 22-25, 2002 , 2002 .

[5]  Vladimir Lifschitz,et al.  ON THE SEMANTICS OF STRIPS , 1987 .

[6]  Patrick Brézillon,et al.  Lecture Notes in Artificial Intelligence , 1999 .

[7]  Leora Morgenstem.  Knowledge preconditions for actions and plans , 1987, IJCAI 1987.

[8]  Moshe Y. Vardi.  Branching vs. Linear Time: Final Showdown , 2001, TACAS.

[9]  Milind Tambe,et al.  Intelligent Agents VIII , 2002, Lecture Notes in Computer Science.

[10]  Pierre-Yves Schobbens,et al.  Agents and Roles: Refinement in Alternating-Time Temporal Logic , 2001, ATAL.

[11]  E. Allen Emerson,et al.  Temporal and Modal Logic , 1991, Handbook of Theoretical Computer Science, Volume B: Formal Models and Sematics.

[12]  Thomas A. Henzinger,et al.  Reactive Modules , 1999, Formal Methods Syst. Des..

[13]  Nuel Belnap,et al.  The deliberative stit: A study of action, omission, ability, and obligation , 1995, J. Philos. Log..

[14]  V. Goranko.  Coalition games and alternating temporal logics , 2001 .

[15]  Robert C. Moore.  Reasoning About Knowledge and Action , 1977, IJCAI.

[16]  Michael Wooldridge,et al.  Tractable multiagent planning for epistemic goals , 2002, AAMAS '02.

[17]  Nicholas R. Jennings,et al.  Intelligent agents: theory and practice , 1995, The Knowledge Engineering Review.

[18]  James A. Hendler,et al.  Readings in Planning , 1994 .

[19]  Mark A. Brown.  On the logic of ability , 1988, J. Philos. Log..

[20]  Marc Pauly,et al.  A Modal Logic for Coalitional Power in Games , 2002, J. Log. Comput..

[21]  Michael Wooldridge,et al.  Time, Knowledge, and Cooperation: Alternating-Time Temporal Epistemic Logic and Its Applications , 2002, KI.

[22]  Richard Fikes,et al.  STRIPS: A New Approach to the Application of Theorem Proving to Problem Solving , 1971, IJCAI.

[23]  M. de Rijke,et al.  Modal Logic , 2001, Cambridge Tracts in Theoretical Computer Science.

[24]  Stephan Merz,et al.  Model Checking , 2000 .

[25]  H. Keiding,et al.  Effectivity functions in social choice , 1991 .

[26]  Leora Morgenstern,et al.  Knowledge Preconditions for Actions and Plans , 1988, IJCAI.

[27]  Thomas A. Henzinger,et al.  MOCHA: Modularity in Model Checking , 1998, CAV.

[28]  Max J. Cresswell,et al.  A New Introduction to Modal Logic , 1998 .

[29]  Philippe Schnoebelen,et al.  The Complexity of Temporal Logic Model Checking , 2002, Advances in Modal Logic.

[30]  C. Pollard,et al.  Center for the Study of Language and Information , 2022 .

[31]  Robert C. Moore.  A Formal Theory of Knowledge and Action , 1984 .

[32]  Thomas A. Henzinger,et al.  Alternating-time temporal logic , 1997, Proceedings 38th Annual Symposium on Foundations of Computer Science.

[33]  Cees Witteveen,et al.  Boolean games , 2001 .

[34]  Brian F. Chellas.  On bringing it about , 1995, J. Philos. Log..

[35]  R. Goldblatt.  Logics of Time and Computation , 1987 .

[36]  Michael Wooldridge,et al.  Logic for Mechanism Design A Manifesto , 2003 .

[37]  Marc Pauly,et al.  Logic for social software , 2000 .

[38]  Michael Wooldridge,et al.  Reasoning about rational agents , 2000, Intelligent robots and autonomous agents.

[39]  M. Wooldridge,et al.  Model checking cooperation, knowledge, and time—a case study , 2003 .

[40]  Govert van Drimmelen,et al.  Satisfiability in Alternating-time Temporal Logic , 2003, LICS.

[41]  Michael Wooldridge,et al.  Cooperation, Knowledge, and Time: Alternating-time Temporal Epistemic Logic and its Applications , 2003, Stud Logica.

[42]  Jerzy Tiuryn,et al.  Dynamic logic , 2001, SIGA.

[43]  Krister Segerberg,et al.  Getting started: Beginnings in the logic of action , 1992, Stud Logica.

[44]  Leora Morgenstern,et al.  A First Order Theory of Planning, Knowledge, and Action , 1986, TARK.

[45]  Wolfgang Thomas,et al.  Handbook of Theoretical Computer Science, Volume B: Formal Models and Semantics , 1990 .

[46]  Yde Venema,et al.  Dynamic Logic by David Harel, Dexter Kozen and Jerzy Tiuryn. The MIT Press, Cambridge, Massachusetts. Hardback: ISBN 0–262–08289–6, $50, xv + 459 pages , 2002, Theory and Practice of Logic Programming.

[47]  Michael Wooldridge,et al.  Time, Knowledge, and Cooperation: Alternating-Time Temporal Epistemic Logic and Its Applications , 2002, COORDINATION.

[48]  Michael Wooldridge,et al.  Intelligent agents: theory and practice The Knowledge Engineering Review , 1995 .

[49]  Nils J. Nilsson,et al.  Artificial Intelligence , 1974, IFIP Congress.

[50]  Nicholas R. Jennings,et al.  The Cooperative Problem-solving Process , 1999, J. Log. Comput..

[51]  Ariel Rubinstein,et al.  A Course in Game Theory , 1995 .

[52]  Jan van Leeuwen,et al.  Handbook of Theoretical Computer Science, Vol. B: Formal Models and Semantics , 1994 .