Distributed Knowledge Justification Logics

Justification logics are a family of modal epistemic logics which enables us to reasoning about justifications and evidences. In this paper, we introduce evidence-based multi-agent distributed knowledge logics, called distributed knowledge justification logics. The language of our justification logics contain evidence-based knowledge operators for individual agents and for distributed knowledge , which are interpreted respectively as “t is a justification that agent i accepts for F”, and “t is a justification that all agents accept for F if they combine their knowledge and justifications”. We study basic properties of our logics and prove the conservativity of distributed knowledge justification logics over multi-agent justification logics. We present Kripke style models, pseudo-Fitting and Fitting models, as well as Mkrtychev models (single world Fitting models) and prove soundness and completeness theorems. We also find a class of Fitting models which satisfies the principle of full communication. Finally, we establish the realization theorem, which states that distributed knowledge justification logics can be embedded into the modal distributed knowledge logics, and vise versa.

[1]  Thomas Studer,et al.  Realizing public announcements by justifications , 2014, J. Comput. Syst. Sci..

[2]  T. Studer.  Justification logic, inference tracking, and data privacy , 2013 .

[3]  Bryan Renne.  Multi-agent Justification Logic: communication and evidence elimination , 2011, Synthese.

[4]  John-Jules Ch. Meyer,et al.  A Complete Epistemic Logic for Multiple Agents , 1997 .

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

[6]  Roman Kuznets,et al.  Realization for justification logics via nested sequents: Modularity through embedding , 2012, Ann. Pure Appl. Log..

[7]  Thomas Studer,et al.  Justifications for common knowledge , 2010, J. Appl. Non Class. Logics.

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

[9]  Thomas Studer.  An Application of Justification Logic to Protocol Verification , 2011, 2011 Seventh International Conference on Computational Intelligence and Security.

[10]  John-Jules Ch. Meyer,et al.  Making Some Issues of Implicit Knowledge Explicit , 1992, Int. J. Found. Comput. Sci..

[11]  John-Jules Ch. Meyer,et al.  Group knowledge is not always distributed (neither is it always implicit) ? ? This is an improved an , 1999 .

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

[13]  Bryan Renne,et al.  Public communication in justification logic , 2011, J. Log. Comput..

[14]  W. van der Hoek,et al.  A Complete Epistemic Logic for Multiple Agents: Combining Distributed and Common Knowledge , 1996 .

[15]  Melvin Fitting,et al.  The logic of proofs, semantically , 2005, Ann. Pure Appl. Log..

[16]  Ioan Alfred Letia,et al.  Arguing with Justifications between Collaborating Agents , 2011, ArgMAS.

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

[18]  Joseph Y. Halpern,et al.  Knowledge and common knowledge in a distributed environment , 1984, JACM.

[19]  Melvin Fitting,et al.  Justification logics, logics of knowledge, and conservativity , 2008, Annals of Mathematics and Artificial Intelligence.

[20]  Sergei N. Artëmov.  THE LOGIC OF JUSTIFICATION , 2008, The Review of Symbolic Logic.

[21]  Meghdad Ghari.  Distributed Knowledge with Justifications , 2011, ESSLLI Student Sessions.

[22]  Sergei N. Artëmov.  Tracking Evidence , 2010, Fields of Logic and Computation.

[23]  Floris Roelofsen,et al.  Distributed knowledge , 2007, J. Appl. Non Class. Logics.

[24]  Alexey Mkrtychev,et al.  Models for the Logic of Proofs , 1997, LFCS.

[25]  Joseph Y. Halpern,et al.  A Guide to the Modal Logics of Knowledge and Belief: Preliminary Draft , 1985, IJCAI.

[26]  Ronald Fagin,et al.  What can machines know?: On the properties of knowledge in distributed systems , 1992, JACM.

[27]  Bryan Renne,et al.  Evidence elimination in multi-agent justification logic , 2009, TARK '09.

[28]  Aviad Heifetz.  Proceedings of the 12th Conference on Theoretical Aspects of Rationality and Knowledge (TARK-2009), Stanford, CA, USA, July 6-8, 2009 , 2009, TARK.

[29]  Lassiter Daniel,et al.  New Directions in Logic, Language and Computation: Esslli 2010 and Esslli 2011 Student Sessions. Selected Papers , 2012 .

[30]  Tatiana Yavorskaya,et al.  Interacting Explicit Evidence Systems , 2008, Theory of Computing Systems.

[31]  Sergei N. Artëmov.  Explicit provability and constructive semantics , 2001, Bull. Symb. Log..

[32]  Sergei N. Artëmov,et al.  Complexity issues in justification logic , 2008 .

[33]  Iyad Rahwan,et al.  Argumentation in Multi-Agent Systems: 8th International Workshop, ArgMAS 2011, Taipei, Taiwan, May 2011, Revised Selected Papers , 2012 .

[34]  Michael Bacharach,et al.  Epistemic Logic and the Theory of Games and Decisions , 2011 .