On Limited Non-Prioritised Belief Revision Operators with Dynamic Scope

The research on non-prioritized revision studies revision operators which do not accept all new beliefs. In this paper, we contribute to this line of research by introducing the concept of dynamic-limited revision, which are revisions expressible by a total preorder over a limited set of worlds. For a belief change operator, we consider the scope, which consists of those beliefs which yield success of revision. We show that for each set satisfying single sentence closure and disjunction completeness there exists a dynamic-limited revision having the union of this set with the beliefs set as scope. We investigate iteration postulates for belief and scope dynamics and characterise them for dynamic-limited revision. As an application, we employ dynamic-limited revision to studying belief revision in the context of so-called inherent beliefs, which are beliefs globally accepted by the agent. This leads to revision operators which we call inherence-limited. We present a representation theorem for inherence-limited revision, and we compare these operators and dynamic-limited revision with the closely related credible-limited revision operators.

[1]  Gabriele Kern-Isberner,et al.  Strong Syntax Splitting for Iterated Belief Revision , 2017, IJCAI.

[2]  Richard Booth,et al.  Admissible and Restrained Revision , 2006, J. Artif. Intell. Res..

[3]  Michael Thielscher,et al.  Iterated Belief Revision, Revised , 2005, IJCAI.

[4]  John Cantwell,et al.  Credibility limited revision , 2001, Journal of Symbolic Logic.

[5]  Christoph Beierle,et al.  Decrement Operators in Belief Change , 2019, ECSQARU.

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

[7]  Judea Pearl,et al.  On the Logic of Iterated Belief Revision , 1994, Artif. Intell..

[8]  Richard Booth,et al.  Credibility-Limited Revision Operators in Propositional Logic , 2012, KR.

[9]  Jean-Marie Lagniez,et al.  On Computational Aspects of Iterated Belief Change , 2020, IJCAI.

[10]  Norman Y. Foo,et al.  Relevance in belief revision , 2015, Artif. Intell..

[11]  Marco Garapa,et al.  Studies in Credibility-Limited Base Revision , 2018, KR.

[12]  Richard Booth,et al.  On the Logic of Iterated Non-prioritised Revision , 2002, WCII.

[13]  Paolo Liberatore,et al.  The Complexity of Iterated Belief Revision , 1997, ICDT.

[14]  Christoph Beierle,et al.  Cognitive Logics - Features, Formalisms, and Challenges , 2020, ECAI.

[15]  Sébastien Konieczny,et al.  Non-Prioritized Iterated Revision: Improvement via Incremental Belief Merging , 2020, KR.

[16]  Richard Booth,et al.  Credibility-Limited Improvement Operators , 2014, ECAI.

[17]  Sébastien Konieczny,et al.  Improvement Operators , 2008, KR.

[18]  Richard Booth,et al.  How to Revise a Total Preorder , 2011, J. Philos. Log..

[19]  Sébastien Konieczny,et al.  Taxonomy of Improvement Operators and the Problem of Minimal Change , 2022 .

[20]  Sebastian Rudolph,et al.  A General Katsuno-Mendelzon-Style Characterization of AGM Belief Base Revision for Arbitrary Monotonic Logics , 2021, ArXiv.

[21]  S. Hansson.  A Survey of non-Prioritized Belief Revision , 1999 .