Combinations of Modal Logics

There is increasing use of combinations of modal logics in bothfoundational and applied research areas. This article provides anintroduction to both the principles of such combinations and to thevariety of techniques that have been developed for them. In addition,the article outlines many key research problems yet to be tackledwithin this callenging area of work.

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

[2]  Clare Dixon,et al.  Temporal resolution using a breadth-first search algorithm , 1998, Annals of Mathematics and Artificial Intelligence.

[3]  R. Schmidt.  Optimised modal translation and resolution , 1997 .

[4]  M. de Rijke,et al.  Encoding Two-Valued Nonclassical Logics in Classical Logic , 2001, Handbook of Automated Reasoning.

[5]  Carole A. Goble,et al.  TAMBIS: Transparent Access to Multiple Bioinformatics Information Sources , 1998, ISMB.

[6]  Ullrich Hustadt.  Resolution based decision procedures for subclasses of first-order logic , 1999 .

[7]  Grigori Mints,et al.  Gentzen-type systems and resolution rules. Part I. Propositional logic , 1990, Conference on Computer Logic.

[8]  John-Jules Ch. Meyer,et al.  Formalising Motivational Attitudes of Agents , 1995, ATAL.

[9]  F. Wolter,et al.  Temporalizing Description Logics , 1998, FroCoS.

[10]  Peter A Flach.  Principles of Knowledge Representation and Reasoning: Proceedings ofg the Sixth International Conference (KR'98) , 1998 .

[11]  Hans Jürgen Ohlbach,et al.  Semantics-Based Translation Methods for Modal Logics , 1991, J. Log. Comput..

[12]  Klaus Schild,et al.  A Correspondence Theory for Terminological Logics: Preliminary Report , 1991, IJCAI.

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

[14]  Clare Dixon,et al.  Clausal Resolution for Logics of Time and Knowledge with Synchrony and Perfect Recall , 2000 .

[15]  Nicholas R. Jennings,et al.  Intelligent agents: theory and practice , 1995, The Knowledge Engineering Review.

[16]  Enrico Franconi,et al.  Temporal Description Logics , 2005, Handbook of Temporal Reasoning in Artificial Intelligence.

[17]  Ulrike Sattler,et al.  A Concept Language Extended with Different Kinds of Transitive Roles , 1996, KI.

[18]  Enrico Franconi,et al.  A survey of temporal extensions of description logics , 2001, Annals of Mathematics and Artificial Intelligence.

[19]  Ullrich Hustadt,et al.  Using Resolution for Testing Modal Satisfiability and Building Models , 2002, Journal of Automated Reasoning.

[20]  Michael Fisher,et al.  A resolution method for CTL branching-time temporal logic , 1997, Proceedings of TIME '97: 4th International Workshop on Temporal Representation and Reasoning.

[21]  Christian G. Fermüller,et al.  Resolution Decision Procedures , 2001, Handbook of Automated Reasoning.

[22]  M. de Rijke,et al.  Spatial Reasoning for Image Retrieval , 1999, Description Logics.

[23]  Renate A. Schmidt.  Decidability by Resolution for Propositional Modal Logics , 2004, Journal of Automated Reasoning.

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

[25]  Ullrich Hustadt,et al.  Issues of Decidability for Description Logics in the Framework of Resolution , 1998, FTP.

[26]  Diego Calvanese,et al.  Dwq : Esprit Long Term Research Project, No 22469 on the Decidability of Query Containment under Constraints on the Decidability of Query Containment under Constraints , 2022 .

[27]  Margus Veanes,et al.  The two-variable guarded fragment with transitive relations , 1999, Proceedings. 14th Symposium on Logic in Computer Science (Cat. No. PR00158).

[28]  Enrico Franconi,et al.  Temporal Entity-Relationship Modeling with Description Logics , 1999 .

[29]  Andreas Nonnengart.  A resolution-based calculus for temporal logics , 1995 .

[30]  Michael Fisher,et al.  Programming Resource-Bounded Deliberative Agents , 1999, IJCAI.

[31]  Yoav Shoham,et al.  A propositional modal logic of time intervals , 1991, JACM.

[32]  Marcus Kracht,et al.  Highway to the Danger Zone , 1995, J. Log. Comput..

[33]  Michael Fisher,et al.  Implementing BDI-like Systems by Direct Execution , 1997, IJCAI.

[34]  Joseph Y. Halpern,et al.  The Complexity of Reasoning about Knowledge and Time. I. Lower Bounds , 1989, J. Comput. Syst. Sci..

[35]  J.F.A.K. van Benthem,et al.  Modal Correspondence Theory , 1977 .

[36]  Dov M. Gabbay,et al.  Adding a temporal dimension to a logic system , 1992, J. Log. Lang. Inf..

[37]  Ian Horrocks,et al.  The GRAIL concept modelling language for medical terminology , 1997, Artif. Intell. Medicine.

[38]  Ullrich Hustadt,et al.  Maslov's Class K Revisited , 1999, CADE.

[39]  Ullrich Hustadt,et al.  On the Relation of Resolution and Tableaux Proof Systems for Description Logics , 1999, IJCAI.

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

[41]  Edith Hemaspaandra.  Complexity transfer for modal logic , 1994, Proceedings Ninth Annual IEEE Symposium on Logic in Computer Science.

[42]  Marcus Kracht,et al.  Simulation and Transfer Results in Modal Logic – A Survey , 1997, Stud Logica.

[43]  Ian Horrocks,et al.  FaCT and iFaCT , 1999, Description Logics.

[44]  W. Hoek,et al.  An Integrated Modal Approach to Rational Agents , 1999 .

[45]  Clare Dixon,et al.  Removing irrelevant information in temporal resolution proofs , 1999, J. Exp. Theor. Artif. Intell..

[46]  Clare Dixon,et al.  Search Strategies for Resolution in Temporal Logics , 1996, CADE.

[47]  Michael Wooldridge,et al.  Resolution for Temporal Logics of Knowledge , 1998, J. Log. Comput..

[48]  Harald Ganzinger,et al.  A Resolution-Based Decision Procedure for Extensions of K4 , 1998, Advances in Modal Logic.

[49]  Michael Fisher,et al.  A Normal Form for Temporal Logics and its Applications in Theorem-Proving and Execution , 1997, J. Log. Comput..

[50]  Brandon Bennett,et al.  Modal Logics for Qualitative Spatial Reasoning , 1996, Log. J. IGPL.

[51]  Ian Horrocks,et al.  Using an Expressive Description Logic: FaCT or Fiction? , 1998, KR.

[52]  Enrico Franconi,et al.  Representing a robotic domain using temporal description logics , 1999, Artif. Intell. Eng. Des. Anal. Manuf..

[53]  Michael Wooldridge,et al.  A Tableau-Based Proof Method for Temporal Logics of Knowledge and Belief , 1998, J. Appl. Non Class. Logics.

[54]  Peter F. Patel-Schneider,et al.  DLP System Description , 1998, Description Logics.

[55]  Giuseppe De Giacomo,et al.  Tableaux and Algorithms for Propositional Dynamic Logic with Converse , 1996, CADE.

[56]  Clare Dixon,et al.  Clausal temporal resolution , 1999, TOCL.

[57]  Diego Calvanese,et al.  Description Logic Framework for Information Integration , 1998, KR.

[58]  Clare Dixon,et al.  Normal Forms and Proofs in Combined Modal and Temporal Logics , 2000, FroCoS.

[59]  Enrico Franconi,et al.  A Temporal Description Logic for Reasoning about Actions and Plans , 1998, J. Artif. Intell. Res..

[60]  Dov M. Gabbay,et al.  Fibring Semantic Tableaux , 1998, TABLEAUX.

[61]  Patrice Enjalbert,et al.  Modal Theorem Proving: An Equational Viewpoint , 1989, IJCAI.

[62]  Bernhard Nebel,et al.  On the Complexity of Qualitative Spatial Reasoning: A Maximal Tractable Fragment of the Region Connection Calculus , 1999, Artif. Intell..

[63]  Joseph Y. Halpern,et al.  Reasoning about knowledge and time in asynchronous systems , 1988, STOC '88.

[64]  M. de Rijke,et al.  Description and/or Hybrid Logics , 2000 .

[65]  Frank Wolter,et al.  Modal Description Logics: Modalizing Roles , 1999, Fundam. Informaticae.

[66]  Renate A. Schmidt,et al.  Functional Translation and Second-Order Frame Properties of Modal Logics , 1997, J. Log. Comput..

[67]  Enrico Franconi,et al.  Temporal ER Modeling with Description Logics , 1999, ER.

[68]  Maarten de Rijke,et al.  Prefixed Resolution: A Resolution Method for Modal and Description Logics , 1999, CADE.

[69]  Michael Fisher,et al.  A Resolution Method for Temporal Logic , 1991, IJCAI.

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

[71]  Brandon Bennett,et al.  Logical representations for automated reasoning about spatial relationships , 1997 .

[72]  Anand S. Rao,et al.  Decision Procedures for Propositional Linear-Time Belief-Desire-Intention Logics , 1995, ATAL.

[73]  Ian Horrocks.  The FaCT System , 1998, TABLEAUX.

[74]  H. Ganzinger,et al.  A theory of resolution , 1997 .

[75]  Enrico Franconi,et al.  A Temporal Description Logic for Reasoning over Conceptual Schemas and Queries , 2002, JELIA.

[76]  Ian Horrocks,et al.  A Description Logic with Transitive and Inverse Roles and Role Hierarchies , 1999, J. Log. Comput..

[77]  Klaus Schild,et al.  Combining Terminological Logics with Tense Logic , 1993, EPIA.