Introspection as an action in relational models

Abstract This work studies positive and negative introspection not as ‘static’ properties an agent might or might not have, but rather as epistemic actions that change the agent's knowledge. The proposed actions include not only operations for achieving full introspection (first with respect to all formulas, and then with respect to a particular χ), but also acts for increasing the agent's introspection by only one degree. In all cases, the actions are represented as model update operations, with matching modalities for expressing the operations' effects. Sound and complete axiom systems are provided in most cases, and some properties of the operations are explored.

[1]  Ho Ngoc Duc,et al.  Reasoning About Rational, But Not Logically Omniscient, Agents , 1997, J. Log. Comput..

[2]  Fernando R. Velázquez-Quesada.  Explicit and Implicit Knowledge in Neighbourhood Models , 2013, LORI.

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

[4]  Hans van Ditmarsch,et al.  The Secret of My Success , 2006, Synthese.

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

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

[7]  Johan van Benthem,et al.  The dynamics of awareness , 2010, Synthese.

[8]  Fernando R. Velázquez-Quesada,et al.  Dynamic Epistemic Logics of Introspection , 2017, DALI@TABLEAUX.

[9]  Jelle Gerbrandy,et al.  The Surprise Examination in Dynamic Epistemic Logic , 2007, Synthese.

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

[11]  Johan van Benthem,et al.  Dynamic Logics of Evidence-Based Beliefs , 2011, Stud Logica.

[12]  Timothy Williamson,et al.  Knowledge and Its Limits , 2000 .

[13]  Davide Grossi,et al.  Syntactic awareness in logical dynamics , 2015, Synthese.

[14]  Joseph Y. Halpern,et al.  The complexity of reasoning about knowledge and time , 1986, STOC '86.

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

[16]  Giuseppe De Giacomo.  Eliminating “converse” from converse PDL , 1996, J. Log. Lang. Inf..

[17]  Mark Jago,et al.  Epistemic Logic for Rule-Based Agents , 2009, J. Log. Lang. Inf..

[18]  Brian F. Chellas.  Modal Logic: Normal systems of modal logic , 1980 .

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

[20]  Jerzy Tiuryn,et al.  Dynamic logic , 2001, SIGA.

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

[22]  Alexandru Baltag,et al.  A qualitative theory of dynamic interactive belief revision , 2008 .

[23]  Wesley H. Holliday,et al.  Moorean Phenomena in Epistemic Logic , 2010, Advances in Modal Logic.

[24]  Fernando R. Velázquez-Quesada,et al.  Reliability-based preference dynamics: lexicographic upgrade , 2017, J. Log. Comput..

[25]  Barteld Kooi,et al.  ARROW UPDATE LOGIC , 2011, The Review of Symbolic Logic.

[26]  Risto Hilpinen,et al.  Knowing that one knows and the classical definition of knowledge , 1970, Synthese.

[27]  Luis Fariñas del Cerro,et al.  Global and Local Graph Modifiers , 2009, M4M.

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

[29]  Ramaswamy Ramanujam,et al.  A Knowledge Based Semantics of Messages , 2003, J. Log. Lang. Inf..

[30]  John P. Burgess,et al.  Basic Tense Logic , 1984 .

[31]  Jaakko Hintikka,et al.  Time And Modality , 1958 .

[32]  A. Perea.  Epistemic Game Theory: Reasoning and Choice , 2012 .

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

[34]  Carlos Areces,et al.  Relation-changing modal operators , 2015, Log. J. IGPL.

[35]  Raul Fervari.  Relation-changing modal logics , 2014 .

[36]  Jelle Gerbrandy,et al.  Reasoning about Information Change , 1997, J. Log. Lang. Inf..

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

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

[39]  Anthony S. Gillies,et al.  A New Solution to Moore's Paradox , 2001 .

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

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

[42]  Richmond Thomason,et al.  Independence of the Dual Axiom in Modal K with Primitive ◊ , 2018, Notre Dame J. Formal Log..

[43]  Natasha Alechina,et al.  The Dynamics of Syntactic Knowledge , 2006, J. Log. Comput..

[44]  Fernando R. Velázquez-Quesada,et al.  A Note on Reliability-Based Preference Dynamics , 2015, LORI.

[45]  Robert Stalnaker,et al.  The problem of logical omniscience, I , 1991, Synthese.

[46]  Boudewijn de Bruin,et al.  Explaining Games: The Epistemic Programme in Game Theory , 2010 .

[47]  Denis Bonnay,et al.  Knowing One’s Limits: An Analysis in Centered Dynamic Epistemic Logic , 2011 .

[48]  Denis Bonnay,et al.  Inexact Knowledge with Introspection , 2009, J. Philos. Log..

[49]  Johan van Benthem,et al.  What one may come to know , 2004 .

[50]  Robert Stalnaker.  On Logics of Knowledge and Belief , 2006 .

[51]  Jeffrey D. Ullman,et al.  Introduction to Automata Theory, Languages and Computation , 1979 .

[52]  Rohit Parikh,et al.  The Completeness of Propositional Dynamic Logic , 1978, MFCS.

[53]  Risto Hilpinen,et al.  Review: E. J. Lemmon, If I Know, do I Know that I Know? , 1973 .

[54]  Carlos Areces,et al.  Moving Arrows and Four Model Checking Results , 2012, WoLLIC.

[55]  Johan van Benthem,et al.  An Essay on Sabotage and Obstruction , 2005, Mechanizing Mathematical Reasoning.

[56]  Moshe Y. Vardi.  On Epistemic Logic and Logical Omniscience , 1986, TARK.