Conference Paper

Horn Complements: Towards Horn-to-Horn Belief Revision.

Conference: Proceedings of the Twenty-Third AAAI Conference on Artificial Intelligence, AAAI 2008, Chicago, Illinois, USA, July 13-17, 2008
Source: DBLP


Horn-to-Horn belief revision asks for the revision of a Horn knowledge base such that the revised knowledge base is also Horn. Horn knowledge bases are important whenever one is concerned with efficiency--of computing inferences, of knowledge acquisition, etc. Horn-to-Horn belief revision could be of interest, in particular, as a component of any efficient system requiring large commonsense knowledge bases that may need revisions because, for example, new contradictory information is acquired. Recent results on belief revision for general logics show that the existence of a belief contraction operator satisfying the generalized AGM postulates is equivalent to the existence of a complement. Here we provide a first step towards efficient Horn-to-Horn belief revision, by characterizing the existence of a complement of a Horn consequence of a Horn knowledge base. A complement exists if and only if the Horn consequence is not the consequence of a modified knowledge base obtained from the original by an operation called body building. This characterization leads to the efficient construction of a complement whenever it exists.

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Available from: Balazs Szorenyi, Jun 25, 2014
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    • "(Liberatore 2000) considers the problem of compact representation for revision in the Horn case. Basically, given a knowledge base K and formula φ, both Horn, the main problem addressed is whether the knowledge base, revised according to a given operator, can be expressed by a propositional formula whose size is polynomial with respect to the sizes of K and φ. (Langlois et al. 2008) approaches the study of revising Horn formulas by characterising the existence of a complement of a Horn consequence; such a complement corresponds to the result of a contraction operator. This work may be seen as a specific instance of a general framework developed in (Flouris, Plexousakis, and Antoniou 2004). "
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    ABSTRACT: Standard approachs to belief change assume that the underlying logic contains classical propositional logic. Recently there has been interest in investigating approaches to belief change, specifically contraction, in which the underlying logic is not as expressive as full propositional logic. In this paper we consider approaches to belief contraction in Horn knowledge bases. We develop two broad approaches for Horn contraction, corresponding to the two major approaches in belief change, based on Horn belief sets and Horn belief bases. We argue that previous approaches, which have taken Horn remainder sets as a starting point, have undesirable properties, and moreover that not all desirable Horn contraction functions are captured by these approaches. This is shown in part by examining model-theoretic considerations involving Horn contraction. For Horn belief set contraction, we develop an account based in terms of weak remainder sets. Maxichoice and partial meet Horn contraction is specified, along with a consideration of package contraction. Following this we consider Horn belief base contraction, in which the underlying knowledge base is not necessarily closed under the Horn consequence relation. Again, approaches to maxichoice and partial meet belief set contraction are developed. In all cases, constructions of the specific operators and sets of postulates are provided, and representation results are obtained. As well, we show that problems arising with earlier work are resolved by these approaches. Copyright © 2010, Association for the Advancement of Artificial Intelligence.
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    • "While there has been some work on revision for Horn clauses [4] [7] [6], it is only recently that attention has been paid to its contraction counterpart. Delgrande [3] investigated two classes of contraction functions for Horn belief sets, viz. "
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    ABSTRACT: We show that Booth et al.'s Horn contraction based on infra-remainder sets corresponds exactly to kernel contraction for belief sets. This result is obtained via a detour through Horn contraction for belief bases, which supports the conjecture that Horn belief change is best viewed as a “hybrid” version of belief set change and belief base change. Moreover, the link with base contraction gives us a more elegant representation result for Horn contraction for belief sets in which a version of the Core-retainment postulate features.
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    • "In recent years there has been considerable interest in dealing with inconsistent ontologies represented in description logics (Baader et al. 2003) but for the most part, this has not been presented explicitly as a contraction problem. While there has been some work on revision for Horn logics (Eiter and Gottlob 1992; Liberatore 2000; Langlois et al. 2008), the only work of importance on Horn contraction, to our knowledge, is that of Delgrande (2008), and this section is mainly devoted to a discussion of his work. "
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    ABSTRACT: Standard belief contraction assumes an underlying logic containing full classical propositional logic, but there are good reasons for considering con- traction in less expressive logics. In this paper we focus on Horn logic. In addition to being of interest in its own right, our choice is moti- vated by the use of Horn logic in several areas, including ontology reasoning in description log- ics. We consider three versions of contraction: entailment-based and inconsistency-based contrac- tion (e-contraction and i-contraction, resp.), intro- duced by Delgrande for Horn logic, and package contraction (p-contraction), studied by Fuhrmann and Hansson for the classical case. We show that the standard basic form of contraction, partial meet, is too strong in the Horn case. We define more appropriate notions of basic contraction for all three types above, and provide associated rep- resentation results in terms of postulates. Our re- sults stand in contrast to Delgrande's conjectures that orderly maxichoice is the appropriate contrac- tion for both e- and i-contraction. Our interest in p-contraction stems from its relationship with an important reasoning task in ontological reasoning: repairing the subsumption hierarchy in EL. This is closely related to p-contraction with sets of basic Horn clauses (Horn clauses of the form p → q). We show that this restricted version of p-contraction can also be represented as i-contraction.
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