Reasoning about Actions Meets Strategic Logics

We introduce ATLEA, a novel extension of Alternating-time Temporal Logic with explicit actions in the object language. ATLEA allows to reason about abilities of agents under commitments to play certain actions. Pre- and postconditions as well as availability and unavailability of actions can be expressed. We show that the multiagent extension of Reiter's solution to the frame problem can be encoded into ATLEA. We also consider an epistemic extension of ATLEA. We demonstrate that the resulting logic is sufficiently expressive to reason about uniform choices of actions. Complexity results for the satisfiability problem of ATLEA and its epistemic extension are given in the paper.

[1]  Anil Nerode,et al.  Logical Foundations of Computer Science, International Symposium, LFCS 2009, Deerfield Beach, FL, USA, January 3-6, 2009. Proceedings , 1994, LFCS.

[2]  Alan Bundy,et al.  Towards Ontology Evolution in Physics , 2008, WoLLIC.

[3]  Jelle Gerbrandy,et al.  Logics of propositional control , 2006, AAMAS '06.

[4]  Emiliano Lorini,et al.  Grounding power on actions and mental attitudes , 2013, Log. J. IGPL.

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

[6]  J. Van Leeuwen,et al.  Handbook of theoretical computer science - Part A: Algorithms and complexity; Part B: Formal models and semantics , 1990 .

[7]  Wojciech Jamroga,et al.  A logic for strategic reasoning , 2005, AAMAS '05.

[8]  Michael Thielscher,et al.  Reasoning robots - the art and science of programming robotic agents , 2005, Applied logic series.

[9]  Vladimir Lifschitz,et al.  A Simple Formalization of Actions Using Circumscription , 1995, IJCAI.

[10]  Thomas Ågotnes,et al.  Action and Knowledge in Alternating-Time Temporal Logic , 2006, Synthese.

[11]  Emiliano Lorini,et al.  A Dynamic Logic of Agency I: STIT, Capabilities and Powers , 2010, J. Log. Lang. Inf..

[12]  Thomas A. Henzinger,et al.  Alternating-time temporal logic , 1999 .

[13]  Michael Wooldridge,et al.  Alternating-time temporal logic with explicit strategies , 2007, TARK '07.

[14]  Gerhard Lakemeyer,et al.  Reasoning about Imperfect Information Games in the Epistemic Situation Calculus , 2010, AAAI.

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

[16]  Valentin Goranko,et al.  Complete axiomatization and decidability of Alternating-time temporal logic , 2006, Theor. Comput. Sci..

[17]  Murray Shanahan.  Solving the frame problem - a mathematical investigation of the common sense law of inertia , 1997 .

[18]  Michael Wooldridge,et al.  On the logic of cooperation and propositional control , 2005, Artif. Intell..

[19]  Martin Lange,et al.  A CTL-Based Logic for Program Abstractions , 2010, WoLLIC.

[20]  Michael Thielscher,et al.  Representing the Knowledge of a Robot , 2000, KR.

[21]  Dirk Walther,et al.  On Satisfiability in ATL with Strategy Contexts , 2012, JELIA.

[22]  Dirk Walther,et al.  Satisfiability of ATEL with Common and Distributed Knowledge is ExpTime-Complete , 2005 .

[23]  Giuseppe De Giacomo,et al.  Situation Calculus Based Programs for Representing and Reasoning about Game Structures , 2010, KR.

[24]  Raymond Reiter,et al.  Natural Actions, Concurrency and Continuous Time in the Situation Calculus , 1996, KR.

[25]  Michael Wooldridge,et al.  ATL Satisfiability is Indeed EXPTIME-complete , 2006, J. Log. Comput..

[26]  Nicolas Markey,et al.  ATL with Strategy Contexts and Bounded Memory , 2009, LFCS.

[27]  Frank Wolter,et al.  Semi-qualitative Reasoning about Distances: A Preliminary Report , 2000, JELIA.

[28]  Michael Gelfond,et al.  Representing Action and Change by Logic Programs , 1993, J. Log. Program..

[29]  Fabio Mogavero.  Reasoning About Strategies , 2013, FSTTCS 2013.

[30]  Andreas Herzig,et al.  From Situation Calculus to Dynamic Epistemic Logic , 2011, J. Log. Comput..

[31]  Stefano Borgo,et al.  Coalitions in Action Logic , 2007, IJCAI.

[32]  Alex M. Andrew,et al.  Knowledge in Action: Logical Foundations for Specifying and Implementing Dynamical Systems , 2002 .