Conference Paper
Horn Complements: Towards HorntoHorn Belief Revision.
Conference: Proceedings of the TwentyThird AAAI Conference on Artificial Intelligence, AAAI 2008, Chicago, Illinois, USA, July 1317, 2008
Source: DBLP

Article: On the Link between Partial Meet, Kernel, and Infra Contraction and its Application to Horn Logic.
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ABSTRACT: Standard belief change assumes an underlying logic containing full classical propositional logic. However, there are good reasons for considering belief change in less expressive logics as well. In this paper we build on recent investigations by Delgrande on contraction for Horn logic. We show that the standard basic form of contraction, partial meet, is too strong in the Horn case. This result stands in contrast to Delgrande’s conjecture that orderly maxichoice is the appropriate form of contraction for Horn logic. We then define a more appropriate notion of basic contraction for the Horn case, influenced by the convexity property holding for full propositional logic and which we refer to as infra contraction. The main contribution of this work is a result which shows that the construction method for Horn contraction for belief sets based on our infra remainder sets corresponds exactly to Hansson’s classical kernel contraction for belief sets, when restricted to Horn logic. This result is obtained via a detour through contraction for belief bases. We prove that kernel contraction for belief bases produces precisely the same results as the belief base version of infra contraction. The use of belief bases to obtain this result provides evidence for the conjecture that Horn belief change is best viewed as a ‘hybrid’ version of belief set change and belief base change. One of the consequences of the link with base contraction is the provision of a representation result for Horn contraction for belief sets in which a version of the Coreretainment postulate features.Journal of Artificial Intelligence Research 01/2011; 42:3153. · 1.06 Impact Factor  [Show abstract] [Hide abstract]
ABSTRACT: Belief revision has been extensively studied in the framework of propositional logic, but just recently revision within fragments of propositional logic has gained attention. Hereby it is not only the belief set and the revision formula which are given within a certain language fragment, but also the result of the revision has to be located in the same fragment. So far, research in this direction has been mainly devoted to the Horn fragment of classical logic. Here we present a general approach to define new revision operators derived from known operators, such that the result of the revision remains in the fragment under consideration. Our approach is not limited to the Horn case but applicable to any fragment of propositional logic where the models of the formulas are closed under a Boolean function. Thus we are able to uniformly treat cases as dual Horn, Krom and affine formulas, as well.Journal of Computer and System Sciences 01/2014; 80(2):427–449. · 1.00 Impact Factor 
Article: Horn clause contraction functions
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ABSTRACT: In classical, AGMstyle 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 modeltheoretic 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 closelyrelated 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 Hornlike reasoning, such as logic programming, rulebased systems, and description logics. Finally, since Horn reasoning is weaker than classical reasoning, this work sheds light on the foundations of belief change.Journal of Artificial Intelligence Research 10/2013; 48(1):475511. · 1.06 Impact Factor
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