A context for belief revision: forward chaining-normal nonmonotomic rule systems

Annals of Pure and Applied Logic 67 (1-3):269-323 (1994)

Abstract

A number of nonmonotonic reasoning formalisms have been introduced to model the set of beliefs of an agent. These include the extensions of a default logic, the stable models of a general logic program, and the extensions of a truth maintenance system among others. In [13] and [16], the authors introduced nonmonotomic rule systems as a nonlogical generalization of all essential features of such formulisms so that theorems applying to all could be proven once and for all. In this paper, we extend Rieter's normal default theories, which have a number of the nice properties which make them a desirable context for belief revision, to the setting of nonmonotonic rule systems. Reiter defined a default theory to be normal if all the rules of the default theory satisfied a simple syntatic condition. However, this simple syntatic condition has no obvious analogue in the setting of nonmonotonic rule systems. Nevertheless, an analysis of the proofs of the main results on normal default theories reveals that the proofs do not rely on the particular syntactic form of the rules but rather on the fact that all rules have a certain consistency property. This led us to extend the notion of normal default theories with respect to a general consistency property. This extended notion of normal default theories, which we call Forward Chaining normal , is easily lifted to nonmonotomic rule systems and hence applies to general logic programs and truth maintenance

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References found in this work

Non-Monotonic Logic I.Drew McDermott & Jon Doyle - 1980 - Artificial Intelligence 13 (1-2):41-72.
A Truth Maintenance System.Jon Doyle - 1979 - Artificial Intelligence 12 (3):231-272.
A Logic for Default Reasoning.Ray Reiter - 1980 - Artificial Intelligence 13 (1-2):81-137.
An Assumption-Based TMS.Johan de Kleer - 1986 - Artificial Intelligence 28 (2):127-162.

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Citations of this work

Logic Programs, Well-Orderings and Forward Chaining.V. W. Marek, A. Nerode & J. B. Remmel - 1999 - Annals of Pure and Applied Logic 96 (1-3):231-276.

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