Not All Those Who Wander Are Lost: Dynamic Epistemic Reasoning in Navigation

In everyday life, people get lost even when they have the map: they simply may not know where they are in the map. However, when moving forward they may have new observations which can help to locate themselves by reasoning. In this paper, we propose and develop a semantic-driven dynamic epistemic framework to handle epistemic reasoning in such navigation scenarios. Our framework can be viewed as a careful blend of dynamic epistemic logic and epistemic temporal logic, thus enjoying features from both frameworks. We made an in-depth study on many model theoretical aspects of the proposed framework and provide a complete axiomatization.

[1]  Blai Bonet,et al.  Planning with Incomplete Information as Heuristic Search in Belief Space , 2000, AIPS.

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

[3]  Lawrence S. Moss,et al.  Logics for Epistemic Programs , 2004, Synthese.

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

[5]  Donald Michie,et al.  On Machine Intelligence , 1974 .

[6]  Robert P. Goldman,et al.  Expressive Planning and Explicit Knowledge , 1996, AIPS.

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

[8]  Wiebe van der Hoek,et al.  Dynamic Epistemic Logic and Knowledge Puzzles , 2007, ICCS.

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

[10]  Michael Wooldridge,et al.  Knowledge and control , 2011, AAMAS.

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

[12]  Andreas Witzel,et al.  The synchronicity of dynamic epistemic logic , 2011, TARK XIII.

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

[14]  Ramaswamy Ramanujam,et al.  Distributed Processes and the Logic of Knowledge , 1985, Logic of Programs.

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

[16]  John-Jules Ch. Meyer,et al.  A Logical Approach to the Dynamics of Commitments , 1999, Artif. Intell..

[17]  Joseph Y. Halpern,et al.  Complete Axiomatizations for Reasoning about Knowledge and Time , 2002, SIAM J. Comput..

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

[19]  Doina Precup,et al.  An Algebraic Approach to Dynamic Epistemic Logic , 2010, Description Logics.

[20]  Alex Horn,et al.  Dynamic Epistemic Algebra with Post-conditions to Reason about Robot Navigation , 2011, WoLLIC.

[21]  Mehrnoosh Sadrzadeh,et al.  Learning in a Changing World, an Algebraic Modal Logical Approach , 2010, AMAST.

[22]  Yanjing Wang,et al.  On axiomatizations of public announcement logic , 2013, Synthese.

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

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

[25]  Hector J. Levesque,et al.  GOLOG: A Logic Programming Language for Dynamic Domains , 1997, J. Log. Program..

[26]  Wiebe van der Hoek,et al.  Dynamic epistemic logic with assignment , 2005, AAMAS '05.