In classical, AGM-style belief change, it is assumed that the underlying logic contains classical propositional logic. This is clearly a limiting assumption, particularly in Artificial Intelligence. Consequently there has been recent interest in studying belief change in approaches where the full expressivity of classical propositional logic is not obtained. In this paper we investigate belief contraction in Horn knowledge bases. We point out that the obvious extension to the Horn case, involving Horn remainder sets as a starting point, is problematic. Not only do Horn remainder sets have undesirable properties, but also some desirable Horn contraction functions are not captured by this approach. For Horn belief set contraction, we develop an account in terms of a model-theoretic characterisation involving weak remainder sets. Maxichoice and partial meet Horn contraction is specified, and we show that the problems arising with earlier work are resolved by these approaches. As well, constructions of the specific operators and sets of postulates are provided, and representation results are obtained. We also examine Horn package contraction, or contraction by a set of formulas. Again, we give a construction and postulate set, linking them via a representation result. Last, we investigate the closely-related notion of forgetting in Horn clauses. This work is arguably interesting since Horn clauses have found widespread use in AI; as well, the results given here may potentially be extended to other areas which make use of Horn-like reasoning, such as logic programming, rule-based systems, and description logics. Finally, since Horn reasoning is weaker than classical reasoning, this work sheds light on the foundations of belief change

No abstract

No abstract

Take-down policy If you believe that this document breaches copyright please contact us providing details, and we will remove access to the work immediately and investigate your claim.

Reasoning and change over inconsistent knowledge bases (KBs) is of utmost relevance in areas like medicine and law. Argumentation may bring the possibility to cope with both problems. Firstly, by constructing an argumentation framework (AF) from the inconsistent KB, we can decide whether to accept or reject a certain claim through the interplay among arguments and counterarguments. Secondly, by handling dynamics of arguments of the AF, we might deal with the dynamics of knowledge of the underlying inconsistent KB.Dynamics of arguments has recently attracted attention and although some approaches have been proposed, a full axiomatization within the theory of belief revision was still missing. A revision arises when we want the argumentation semantics to accept an argument. Argument Theory Change (ATC) encloses the revision operators that modify the AF by analyzing dialectical trees -arguments as nodes and attacks as edges-as the adopted argumentation semantics.In this article, we present a simple approach to ATC based on propositional KBs. This allows to manage change of inconsistent KBs by relying upon classical belief revision, although contrary to it, consistency restoration of the KB is avoided. Subsequently, a set of rationality postulates adapted to argumentation is given, and finally, the proposed model of change is related to the postulates through the corresponding representation theorem. Though we focus on propositional logic, the results can be easily extended to more expressive formalisms such as first-order logic and description logics, to handle evolution of ontologies.