Partial meet pseudo-contractions

Abstract In the AGM paradigm for belief revision, epistemic states are represented by logically closed sets of sentences, the so-called belief sets. An alternative approach uses belief bases, arbitrary sets of sentences. Both approaches have their problems when it comes to contraction operations. Belief bases are more expressive, but, at the same time, they present a serious syntax dependence. Between those two extremes lie a whole gamut of operations called pseudo-contractions, some of which may be interesting alternatives to the classical ones, providing a good balance between syntax dependence and expressivity. In this paper we explore some very natural and general constructions for pseudo-contractions, showing some of their properties and giving their axiomatic characterizations. We also illustrate possible practical scenarios where they can be employed.

[1]  Thomas R. Gruber,et al.  A translation approach to portable ontology specifications , 1993, Knowl. Acquis..

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

[3]  SVEN OVE HANSSON,et al.  Reversing the Levi identity , 1993, J. Philos. Log..

[4]  David Makinson,et al.  On the logic of theory change: Safe contraction , 1985, Stud Logica.

[5]  Allen Newell,et al.  The Knowledge Level , 1989, Artif. Intell..

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

[7]  Sven Ove Hansson.  Kernel Contraction , 1994, J. Symb. Log..

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

[9]  Renata Wassermann,et al.  Approximate Belief Revision , 2001, Log. J. IGPL.

[10]  André Fuhrmann,et al.  The Logic of Theory Change , 1991, Lecture Notes in Computer Science.

[11]  David Makinson,et al.  New studies in deontic logic , 1981 .

[12]  Thomas Andreas Meyer.  Basic Infobase Change , 2001, Stud Logica.

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

[14]  Sven Ove Hansson.  Belief Revision: A dyadic representation of belief , 1992 .

[15]  Sven Ove Hansson,et al.  New operators for theory change , 2008 .

[16]  Franz Baader.  Description Logics , 2009, Reasoning Web.

[17]  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..

[18]  Marco Schaerf,et al.  Tractable Reasoning via Approximation , 1995, Artif. Intell..

[19]  Hector J. Levesque,et al.  A Logic of Implicit and Explicit Belief , 1984, AAAI.

[20]  David Makinson,et al.  On the logic of theory change: Contraction functions and their associated revision functions , 2008 .

[21]  C. E. Alchourrón,et al.  On the logic of theory change: Partial meet contraction and revision functions , 1985 .

[22]  THOMAS ANDREAS MEYER,et al.  Infobase Change: A First Approximation , 2000, J. Log. Lang. Inf..

[23]  Abhaya C. Nayak.  Foundational belief change , 1994, J. Philos. Log..

[24]  Renata Wassermann,et al.  Between Belief Bases and Belief Sets: Partial Meet Contraction , 2015, DARe@IJCAI.

[25]  Sven Ove Hansson,et al.  A Textbook Of Belief Dynamics , 1999 .

[26]  G. Flouris,et al.  On belief change and ontology evolution , 2006 .

[27]  Graham Priest,et al.  The logic of paradox , 1979, J. Philos. Log..

[28]  Bernhard Nebel,et al.  A Knowledge Level Analysis of Belief Revision , 1989, KR.

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

[30]  James P. Delgrande,et al.  Horn Clause Belief Change: Contraction Functions , 2008, KR.

[31]  Thomas R. Gruber,et al.  Toward principles for the design of ontologies used for knowledge sharing? , 1995, Int. J. Hum. Comput. Stud..