Unifying default reasoning and belief revision in a modal framework

doi:10.1016/0004-3702(94)90095-7

Artificial Intelligence

Volume 68, Issue 1, July 1994, Pages 33-85

https://doi.org/10.1016/0004-3702(94)90095-7 Get rights and content

Abstract

We present a logic for reasoning about belief revision in which the process of revising a knowledge base by some sentence is represented with a conditional connective. The conditional is not primitive however; it is defined in terms of two unary modal operators. We show that our notion of revision is equivalent to that determined by the classic AGM postulates. Furthermore, unlike current models of revision, our approach does not require the Limit Assumption. We also present a model for subjunctive query answering that allows the expression of subjunctive or factual premises, integrity constraints, and notions of entrenchment and plausibility. The modal framework we adopt is sufficiently general to allow the expression of other forms of defeasible reasoning, and facilitates the demonstration of some interesting connections between revision, default reasoning and autoepistemic logic. In particular, we show that the normative conditional for default reasoning (developed in a companion paper) and our subjunctive conditional are identical. Default reasoning can thus be viewed as the revision of a theory of expectations in manner that naturally relates priorities of default rules to the entrenchment of expectations.

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The area of belief revision studies how a rational agent may incorporate new information about a domain into its belief corpus. An agent is characterised by a belief state K, and receives a new item of information α which is to be included among its set of beliefs. Revision then is a function from a belief state and a formula to a new belief state.
We propose here a more general framework for belief revision, in which revision is a function from a belief state and a finite set of formulas to a new belief state. In particular, we distinguish revision by the set ${α, β}$ from the set ${α \land β}$ . This seemingly innocuous change has significant ramifications with respect to iterated belief revision. A problem in approaches to iterated belief revision is that, after first revising by a formula and then by a formula that is inconsistent with the first formula, all information in the original formula is lost.
This problem is avoided here in that, in revising by a set of formulas S, the resulting belief state contains not just the information that members of S are believed to be true, but also the counterfactual supposition that if some members of S were later believed to be false, then the remaining members would nonetheless still be believed to be true. Thus if some members of S were in fact later believed to be false, then the other elements of S would still be believed to be true. Hence, we provide a more nuanced approach to belief revision. The general approach, which we call parallel belief revision, is independent of extant approaches to iterated revision. We present first a basic approach to parallel belief revision. Following this we combine the basic approach with an approach due to Jin and Thielscher for iterated revision. Postulates and semantic conditions characterising these approaches are given, and representation results provided. We conclude with a discussion of the possible ramifications of this approach in belief revision in general.
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This paper presents a general, consistency-based framework for expressing belief change. The framework has good formal properties while being well-suited for implementation. For belief revision, informally, in revising a knowledge base K by a sentence α, we begin with α and include as much of K as consistently possible. This is done by expressing K and α in disjoint languages, asserting that the languages agree on the truth values of corresponding atoms wherever consistently possible, and then re-expressing the result in the original language of K. There may be more than one way in which the languages of K and α can be so correlated: in choice revision, one such “extension” represents the revised state; alternately (skeptical) revision consists of the intersection of all such extensions. Contraction is similarly defined although, interestingly, it is not interdefinable with revision.
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Unifying default reasoning and belief revision in a modal framework

Abstract

Int. J. Approx. Reason.

Artif. Intell.

Artif. Intell.

Artif. Intell.

Artif. Intell.

Artif. Intell.

Artif. Intell.

Artif. Intell.

Artif. Intell.

Artif. Intell.

Artif. Intell.

On the logic of theory change: Partial meet contraction and revision functions

J. Symbolic Logic

A logic for hypothetical reasoning

Conditional logics of normality as modal systems

Inaccessible worlds and irrelevance: Preliminary report

Conditional logics for default reasoning and belief revision

Epistemic entrenchment in autoepistemic logic

Fund. Inform.

Revision sequences and nested conditionals

Abduction as belief revision: a model of preferred explanations

Revision by conditional beliefs

Preferred subtheories: an extended logical framework for default reasoning

An introduction to possibilistic and fuzzy logics

On the semantics of updates in databases: preliminary report

Conditionals and changes in belief

Acta Philosophica Fennica