Extending AGM Contraction to Arbitrary Logics

Classic entrenchment-based contraction is not applicable to many useful logics, such as description logics. This is because the semantic construction refers to arbitrary disjunctions of formulas, while many logics do not fully support disjunction. In this paper, we present a new entrenchment-based contraction which does not rely on any logical connectives except conjunction. This contraction is applicable to all fragments of first-order logic that support conjunction. We provide a representation theorem for the contraction which shows that it satisfies all the AGM postulates except for the controversial Recovery Postulate, and is a natural generalisation of entrenchment-based contraction.

[1]  Fachgruppe Philosophie,et al.  Preferential Belief Change Using Generalized Epistemic Entrenchment , 1992 .

[2]  Eduardo L. Fermé,et al.  An Axiomatic Characterization of Ensconcement-Based Contraction , 2008, J. Log. Comput..

[3]  Johanna Völker,et al.  A Kernel Revision Operator for Terminologies - Algorithms and Evaluation , 2008, International Semantic Web Conference.

[4]  Diego Calvanese,et al.  Linking Data to Ontologies , 2008, J. Data Semant..

[5]  Renata Wassermann,et al.  Base Revision for Ontology Debugging , 2009, J. Log. Comput..

[6]  Hans Rott,et al.  Preferential belief change using generalized epistemic entrenchment , 1992, J. Log. Lang. Inf..

[7]  James P. Delgrande,et al.  Belief revision in Horn theories , 2015, Artif. Intell..

[8]  Guilin Qi,et al.  Contraction and Revision over DL-Lite TBoxes , 2014, AAAI.

[9]  M. Panella.  Associate Editor of the Journal of Computer and System Sciences , 2014 .

[10]  Stefan Woltran,et al.  Belief revision within fragments of propositional logic , 2012, J. Comput. Syst. Sci..

[11]  Peter Gärdenfors,et al.  On the logic of theory change: Partial meet contraction and revision functions , 1985, Journal of Symbolic Logic.

[12]  David Makinson,et al.  On the status of the postulate of recovery in the logic of theory change , 1987, J. Philos. Log..

[13]  Ian Horrocks,et al.  The Irresistible SRIQ , 2005, OWLED.

[14]  Richard Booth,et al.  On the Link between Partial Meet, Kernel, and Infra Contraction and its Application to Horn Logic , 2011, J. Artif. Intell. Res..

[15]  Franz Baader,et al.  Pushing the EL Envelope , 2005, IJCAI.

[16]  Nils J. Nilsson,et al.  Artificial Intelligence , 1974, IFIP Congress.

[17]  Diego Calvanese,et al.  The Description Logic Handbook , 2007 .

[18]  Peter Gärdenfors,et al.  Revisions of Knowledge Systems Using Epistemic Entrenchment , 1988, TARK.

[19]  Guilin Qi,et al.  Knowledge Base Revision in Description Logics , 2006, JELIA.

[20]  Sven Ove Hansson,et al.  Changes of disjunctively closed bases , 1993, J. Log. Lang. Inf..

[21]  A. G. Oettinger,et al.  Language and information , 1968 .

[22]  Kewen Wang,et al.  A New Approach to Knowledge Base Revision in DL-Lite , 2010, AAAI.

[23]  James P. Delgrande,et al.  Horn Clause Contraction Functions , 2013, J. Artif. Intell. Res..

[24]  Grigoris Antoniou,et al.  Minimal change: Relevance and recovery revisited , 2013, Artif. Intell..

[25]  P G rdenfors,et al.  Knowledge in flux: modeling the dynamics of epistemic states , 1988 .

[26]  Bart Selman,et al.  Knowledge compilation and theory approximation , 1996, JACM.

[27]  Dan Suciu,et al.  Journal of the ACM , 2006 .

[28]  Peter Gärdenfors,et al.  Knowledge in Flux: Modeling the Dynamics of Epistemic States , 2008 .

[29]  Maurice Pagnucco,et al.  Entrenchment-Based Horn Contraction , 2014, J. Artif. Intell. Res..

[30]  Sven Ove Hansson,et al.  Belief contraction without recovery , 1991, Stud Logica.

[31]  Yehoshua Bar-Hillel,et al.  Language and Information , 1964 .

[32]  Sebastian Rudolph,et al.  Worst-Case Optimal Reasoning for the Horn-DL Fragments of OWL 1 and 2 , 2010, KR.