Direct and Indirect Common Belief

We give informal definitions of the concepts of direct and indirect common belief, illustrating them by an example. We then provide an analysis of these concepts within public announcement logic (PAL). The conceptual distinction between direct common belief and indirect common belief is important because it identifies two social phenomena which rely on different forms of agents’ cognitive capabilities. It is moreover relevant for speech act theory.

[1]  Robert Sugden,et al.  COMMON KNOWLEDGE, SALIENCE AND CONVENTION: A RECONSTRUCTION OF DAVID LEWIS' GAME THEORY , 2003, Economics and Philosophy.

[2]  Cristina Bicchieri,et al.  Self-refuting theories of strategic interaction: A paradox of common knowledge , 1989 .

[3]  Maria Luisa Dalla Chiara,et al.  Knowledge, Belief, and Strategic Interaction , 1992 .

[4]  Sarit Kraus,et al.  Collaborative Plans for Complex Group Action , 1996, Artif. Intell..

[5]  Andreas Herzig,et al.  Tableaux for Public Announcement Logic , 2010, J. Log. Comput..

[6]  Michael E. Bratman,et al.  Shared Cooperative Activity , 1991 .

[7]  Jan A. Plaza,et al.  Logics of public communications , 2007, Synthese.

[8]  Giacomo Sillari,et al.  A Logical Framework for Convention , 2005, Synthese.

[9]  A. Baltag,et al.  Logics for epistemic programs , 2004 .

[10]  Daniel Lehmann,et al.  Knowledge, common knowledge and related puzzles (Extended Summary) , 1984, PODC '84.

[11]  D. Kirsh,et al.  Proceedings of the 25th annual conference of the Cognitive Science Society , 2003 .

[12]  R. Aumann.  Agreeing to disagree. , 1976, Nature cell biology.

[13]  Pierpaolo Battigalli,et al.  Recent results on belief, knowledge and the epistemic foundations of game theory , 1999 .

[14]  Joshua Sack,et al.  Temporal Languages for Epistemic Programs , 2008, J. Log. Lang. Inf..

[15]  Hans van Ditmarsch,et al.  The Russian Cards Problem , 2003, Stud Logica.

[16]  J. Hintikka.  Knowledge and belief , 1962 .

[17]  R. Tuomela.  The Importance of Us: A Philosophical Study of Basic Social Notions , 1995 .

[18]  W. Hoek,et al.  Dynamic Epistemic Logic , 2007 .

[19]  Margaret Gilbert.  On Social Facts , 1989 .

[20]  Giacomo Bonanno,et al.  Common Belief with the Logic of Individual Belief , 2000 .

[21]  David Lewis.  Convention: A Philosophical Study , 1986 .

[22]  Barteld P. Kooi,et al.  Expressivity and completeness for public update logics via reduction axioms , 2007, J. Appl. Non Class. Logics.

[23]  Tomohiro Hoshi,et al.  Dynamic epistemic logic with branching temporal structures , 2009, Synthese.

[24]  M. Bacharach.  Knowledge, belief, and strategic interaction: The acquisition of common knowledge , 1992 .

[25]  W. van der Hoek,et al.  Epistemic logic for AI and computer science , 1995, Cambridge tracts in theoretical computer science.

[26]  J. Searle.  Expression and Meaning: Studies in the Theory of Speech Acts , 1979 .

[27]  F. Ramsey.  General Propositions and Causality , 1931 .

[28]  Raimo Tuomela,et al.  Collective Goals and Communicative Action , 2002, Social Ontology in the Making.

[29]  Emiliano Lorini,et al.  The Prescriptive Destiny of Predictive Attitudes: From Expectations to Norms via Conventions , 2003 .

[30]  Aviad Heifetz.  Iterative and fixed point common belief , 1999, J. Philos. Log..

[31]  B. Webber,et al.  Elements of Discourse Understanding , 1983 .

[32]  Yanjing Wang,et al.  To know or not to know: epistemic approaches to security protocol verification , 2010, Synthese.

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

[34]  Johan van Benthem,et al.  Reduction axioms for epistemic actions , 2004 .

[35]  A. Baltag,et al.  EPISTEMIC LOGIC AND INFORMATION UPDATE , 2008 .