In Praise of Strategies

This programmatic note high-lights a major theme in my lecture notes "Logic in Games"[37]: the need for explicit logics that define agents' strategies, as the drivers of interaction in games. Our text outlines issues, recalls recent results, and raises new open problems. Results are mainly quoted, and the emphasis is on new notions and questions. For more details on the various topics discussed, see the relevant references.

[1]  Wilfrid Hodges,et al.  Logic and Games , 2001 .

[2]  Johan van Benthem,et al.  Rational Dynamics and Epistemic Logic in Games , 2007, IGTR.

[3]  Patrick Girard,et al.  Modal logic for belief and preference change , 2008 .

[4]  G. Fontaine,et al.  Modal fixpoint logic: some model theoretic questions , 2010 .

[5]  Johan van Benthem,et al.  Extensive Games as Process Models , 2002, J. Log. Lang. Inf..

[6]  Jonathan A. Zvesper,et al.  Keep ‘hoping’ for rationality: a solution to the backward induction paradox , 2009, Synthese.

[7]  Bryan Renne,et al.  Propositional Games with Explicit Strategies , 2006, WoLLIC.

[8]  Johan van Benthem,et al.  Merging Frameworks for Interaction , 2009, J. Philos. Log..

[9]  Johan van Benthem,et al.  Dynamic logic of preference upgrade , 2007, J. Appl. Non Class. Logics.

[10]  Johan van Benthem,et al.  Open Problems in Logic and Games , 2005, We Will Show Them!.

[11]  Johan van Benthem,et al.  Game Solution, Epistemic Dynamics and Fixed-Point Logics , 2010, Fundam. Informaticae.

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

[13]  Ming Xu Combinations of Stit and Actions , 2010, J. Log. Lang. Inf..

[14]  J.F.A.K. van Benthem Five Questions on Games , 2007 .

[15]  Lawrence S. Moss,et al.  The Logic of Public Announcements and Common Knowledge and Private Suspicions , 1998, TARK.

[16]  Colin Stirling,et al.  Modal mu-calculi , 2007, Handbook of Modal Logic.

[17]  Giacomo Bonanno,et al.  Axiomatic characterization of the AGM theory of belief revision in a temporal logic , 2007, Artif. Intell..

[18]  Michael Wooldridge,et al.  Extended Modal Logics for Social Software (extended abstract of invited talk) , 2007 .

[19]  Johan van Benthem,et al.  Modelling simultaneous games in dynamic logic , 2008, Synthese.

[20]  Trevor J. M. Bench-Capon,et al.  On the Instantiation of Knowledge Bases in Abstract Argumentation Frameworks , 2013, CLIMA.

[21]  Johan van Benthem,et al.  Logic in Games , 2014 .

[22]  Ronald Fagin,et al.  Knowledge-based programs , 1997, Distributed Computing.

[23]  Ron van der Meyden,et al.  The Dynamic Logic of Permission , 1990, J. Log. Comput..

[24]  Yanjing Wang,et al.  Logic of Information Flow on Communication Channels , 2010, DALT.

[25]  Johan van Benthem,et al.  Dynamic logic for belief revision , 2007, J. Appl. Non Class. Logics.

[26]  Olivier Roy,et al.  Preference logic, conditionals and solution concepts in games , 2005 .

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

[28]  H. Maturana The tree of knowledge , 1987 .

[29]  Fenrong Liu,et al.  Changing for the better : preference dynamics and agent diversity , 2008 .

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

[31]  Nina Gierasimczuk,et al.  Can Doxastic Agents Learn? On the Temporal Structure of Learning , 2009, LORI.

[32]  Johan van Benthem,et al.  Logic Games: From Tools to Models of Interaction , 2011, Proof, Computation and Agency.

[33]  Johan van Benthem,et al.  Everything Else Being Equal: A Modal Logic for Ceteris Paribus Preferences , 2009, J. Philos. Log..

[34]  Yanjing Wang,et al.  Verifying epistemic protocols under common knowledge , 2009, TARK '09.

[35]  Rineke Verbrugge,et al.  Texts in Logic and Games , 2011 .

[36]  J. Benthem Games in dynamic epistemic logic , 2001 .

[37]  Johan van Benthem,et al.  Modal Fixed-Point Logic and Changing Models , 2008, Pillars of Computer Science.

[38]  Artur S. d'Avila Garcez,et al.  We Will Show Them! Essays in Honour of Dov Gabbay, Volume One , 2005, We Will Show Them!.

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

[40]  Martin Hofmann,et al.  Finite Dimensional Vector Spaces Are Complete for Traced Symmetric Monoidal Categories , 2008, Pillars of Computer Science.

[41]  ERIC PACUIT,et al.  REASONING WITH PROTOCOLS UNDER IMPERFECT INFORMATION , 2011, The Review of Symbolic Logic.

[42]  Keith Devlin,et al.  Logic and information , 1991 .

[43]  Yanjing Wang,et al.  Epistemic Modelling and Protocol Dynamics , 2010 .

[44]  Johan van Benthem,et al.  Logical Dynamics of Information and Interaction , 2014 .

[45]  Hans van Ditmarsch,et al.  What will they say?—Public Announcement Games , 2011, Synthese.

[46]  N. Belnap,et al.  Facing the Future: Agents and Choices in Our Indeterminist World , 2001 .

[47]  Fenrong Liu,et al.  Modelling Simultaneous games with Concurrent Dynamic logic , 2007 .

[48]  Johan van Benthem,et al.  Epistemic dynamics and protocol information , 2009 .

[49]  Patrick Blackburn,et al.  Modal logic: a semantic perspective , 2007, Handbook of Modal Logic.

[50]  Jonathan A. Zvesper,et al.  Proof-Theoretic Analysis of Rationality for Strategic Games with Arbitrary Strategy Sets , 2010, CLIMA.

[51]  Sergei N. Artëmov Logic of Proofs: a Unified Semantics for Modality and lambda-Terms , 1998 .

[52]  Nina Gierasimczuk,et al.  UvA-DARE ( Digital Academic Repository ) Knowing one ' s limits : logical analysis of inductive inference , 2010 .

[53]  Rohit Parikh,et al.  Game Logic - An Overview , 2003, Stud Logica.

[54]  Alan Bundy,et al.  Constructing Induction Rules for Deductive Synthesis Proofs , 2006, CLASE.

[55]  Kim G. Larsen,et al.  On Modal Refinement and Consistency , 2007, CONCUR.

[56]  S. Abramsky Semantics of Interaction: an introduction to Game Semantics , 1997 .

[57]  Jonathan A. Zvesper Playing with information , 2010 .

[58]  Felix A. Fischer,et al.  An integrated framework for adaptive reasoning about conversation patterns , 2005, AAMAS '05.

[59]  Sergiu Hart Five Questions on Game Theory , 2007 .

[60]  Olivier Roy,et al.  Agreement Theorems in Dynamic-Epistemic Logic , 2009, TARK '09.

[61]  J. Benthem,et al.  Diversity of Logical Agents in Games , 2004 .

[62]  Ronald Fagin,et al.  Reasoning about knowledge , 1995 .

[63]  A. Gheerbrant Fixed-point logics on trees , 2010 .

[64]  Johan van Benthem,et al.  The Tree of Knowledge in Action: Towards a Common Perspective , 2006, Advances in Modal Logic.

[65]  J. Benthem,et al.  Logics of communication and change , 2006 .

[66]  Johan van Benthem,et al.  Merging frameworks for interaction: DEL and ETL , 2007, TARK '07.

[67]  Alexandru Baltag,et al.  Group belief dynamics under iterated revision: fixed points and cycles of joint upgrades , 2009, TARK '09.

[68]  Frank Wolter,et al.  Handbook of Modal Logic , 2007, Studies in logic and practical reasoning.