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Preferred Answer Sets for Extended Logic Programs
 ARTIFICIAL INTELLIGENCE
, 1998
"... In this paper, we address the issue of how Gelfond and Lifschitz's answer set semantics for extended logic programs can be suitably modified to handle prioritized programs. In such programs an ordering on the program rules is used to express preferences. We show how this ordering can be used ..."
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Cited by 157 (20 self)
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In this paper, we address the issue of how Gelfond and Lifschitz's answer set semantics for extended logic programs can be suitably modified to handle prioritized programs. In such programs an ordering on the program rules is used to express preferences. We show how this ordering can be used to define preferred answer sets and thus to increase the set of consequences of a program. We define a strong and a weak notion of preferred answer sets. The first takes preferences more seriously, while the second guarantees the existence of a preferred answer set for programs possessing at least one answer set. Adding priorities
Prioritizing Default Logic
 Intellectics and Computational Logic — Papers in Honour of Wolfgang Bibel
, 1998
"... INTRODUCTION In nonmonotonic reasoning conflicts among defaults are ubiquitous. For instance, more specific rules may be in conflict with more general ones, a problem which has been studied intensively in the context of inheritance networks (Poole,1985; Touretzky, 1986; Touretzky et al., 1991). Whe ..."
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Cited by 61 (7 self)
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INTRODUCTION In nonmonotonic reasoning conflicts among defaults are ubiquitous. For instance, more specific rules may be in conflict with more general ones, a problem which has been studied intensively in the context of inheritance networks (Poole,1985; Touretzky, 1986; Touretzky et al., 1991). When defaults are used for representing design goals in configuration tasks conflicts naturally arise. The same is true in model based diagnosis where defaults are used to represent the assumption that components typically are ok. In legal reasoning conflicts among rules are very common (Prakken, 1993) and keep many lawyers busy (and rich). The standard nonmontonicformalisms handle such conflicts by generating multiple belief sets. In default logic (Reiter, 1980) and autoepistemic logic (Moore, 1985) these sets are called extensions or expansions, respectively. In circumscription (McCarthy, 1980) the belief sets correspond to different classes of preferred models. Usually, not all of the beli
On the Tractable Counting of Theory Models and its Application to Truth Maintenance and Belief Revision
 Journal of Applied NonClassical Logics
, 2000
"... We address the problem of counting the models of a propositional theory, under incremental changes to the theory. Specifically, we show that if a propositional theory is in a special form that we call smooth, deterministic, decomposable negation normal form (sdDNNF), then for any consistent set of ..."
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Cited by 60 (19 self)
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We address the problem of counting the models of a propositional theory, under incremental changes to the theory. Specifically, we show that if a propositional theory is in a special form that we call smooth, deterministic, decomposable negation normal form (sdDNNF), then for any consistent set of literals S, we can simultaneously count, in time linear in the size of , the models of: [ S; [ S [ flg: for every literal l 62 S; [ S n flg: for every literal l 2 S; [ S n flg [ f:lg: for every literal l 2 S.
A Framework for Compiling Preferences in Logic Programs
 Theory and Practice of Logic Programming
, 2002
"... We introduce a methodology and framework for expressing general preference information in logic programming under the answer set semantics. An ordered logic program is an extended logic program in which rules are named by unique terms, and in which preferences among rules are given by a set of at ..."
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Cited by 58 (18 self)
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We introduce a methodology and framework for expressing general preference information in logic programming under the answer set semantics. An ordered logic program is an extended logic program in which rules are named by unique terms, and in which preferences among rules are given by a set of atoms of the form s t where s and t are names. An ordered logic program is transformed into a second, regular, extended logic program wherein the preferences are respected, in that the answer sets obtained in the transformed program correspond with the preferred answer sets of the original program. Our approach allows the specification of dynamic orderings, in which preferences can appear arbitrarily within a program. Static orderings (in which preferences are external to a logic program) are a trivial restriction of the general dynamic case. First, we develop a specific approach to reasoning with preferences, wherein the preference ordering specifies the order in which rules are to be applied. We then demonstrate the wide range of applicability of our framework by showing how other approaches, among them that of Brewka and Eiter, can be captured within our framework. Since the result of each of these transformations is an extended logic program, Affiliated with the School of Computing Science at Simon Fraser University, Burnaby, Canada.
Knowledge Integration for Description Logics
 In Proceedings of the 7 th International Symposium on Logical Formalizations of Commonsense Reasoning
, 2005
"... Description logic reasoners are able to detect incoherences (such as logical inconsistency and concept unsatisfiability) in knowledge bases, but provide little support for resolving them. We propose to recast techniques for propositional inconsistency management into the description logic setting. W ..."
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Cited by 43 (2 self)
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Description logic reasoners are able to detect incoherences (such as logical inconsistency and concept unsatisfiability) in knowledge bases, but provide little support for resolving them. We propose to recast techniques for propositional inconsistency management into the description logic setting. We show that the additional structure afforded by description logic statements can be used to refine these techniques. Our focus in this paper is on the formal semantics for such techniques, although we do provide highlevel decision procedures for the knowledge integration strategies discussed.
Knowledge Representation with Logic Programs
 DEPT. OF CS OF THE UNIVERSITY OF KOBLENZLANDAU
, 1996
"... In this tutorialoverview, which resulted from a lecture course given by the authors at ..."
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Cited by 38 (6 self)
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In this tutorialoverview, which resulted from a lecture course given by the authors at
Space Efficiency of Propositional Knowledge Representation Formalisms
 IN PROCEEDINGS OF THE FIFTH INTERNATIONAL CONFERENCE ON THE PRINCIPLES OF KNOWLEDGE REPRESENTATION AND REASONING (KR'96
, 2000
"... We investigate the space efficiency of a Propositional Knowledge Representation (PKR) formalism. Intuitively, the space efficiency of a formalism F in representing a certain piece of knowledge #, is the size of the shortest formula of F that represents #. In this paper we assume that knowledge is ..."
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Cited by 31 (5 self)
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We investigate the space efficiency of a Propositional Knowledge Representation (PKR) formalism. Intuitively, the space efficiency of a formalism F in representing a certain piece of knowledge #, is the size of the shortest formula of F that represents #. In this paper we assume that knowledge is either a set of propositional interpretations (models) or a set of propositional formulae (theorems). We provide a formal way of talking about the relative ability of PKR formalisms to compactly represent a set of models or a set of theorems. We introduce two new compactness measures, the corresponding classes, and show that the relative space efficiency of a PKR formalism in representing models/theorems is directly related to such classes. In particular, we consider formalisms for nonmonotonic reasoning, such as circumscription and default logic, as well as belief revision operators and the stable model semantics for logic programs with negation. One interesting result is that formalisms ...
Possibilistic Logic: Complexity and Algorithms
, 1997
"... Possibilistic logic is a logic for reasoning with uncertain and partially inconsistent knowledge bases. Its standard version consists in ranking propositional formulas according to their certainty or priority level, by assigning them lower bounds of necessity values. We give a survey of automated de ..."
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Cited by 30 (0 self)
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Possibilistic logic is a logic for reasoning with uncertain and partially inconsistent knowledge bases. Its standard version consists in ranking propositional formulas according to their certainty or priority level, by assigning them lower bounds of necessity values. We give a survey of automated deduction techniques for standard possibilistic logic, together with complexity results. We focus on the extensions of resolution (Section 3) and of the Davis and Putnam procedure (Section 4). In Section 5 we consider extended versions and variants of possibilistic logic. We conclude by listing the related research topics, the applicative impact of this work and further research issues. 1 Introduction Possibilistic logic is a logic of uncertainty tailored for reasoning under incomplete and partially inconsistent knowledge. At the syntactical level it handles formulae of propositional or firstorder classical logic, to which are attached lower bounds of socalled degrees of necessity and possib...
An Algorithm for Belief Revision
 In Proceedings of the Seventh International Conference on Principles of Knowledge Representation and Reasoning (KR2000
, 2000
"... In this paper we show that a particular construction of belief revision operator is equivalent to the standard method for computing consistencybased diagnosis. We show how a diagnosis problem can be translated into a problem of belief revision and show how kernel constructions for revision op ..."
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Cited by 27 (6 self)
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In this paper we show that a particular construction of belief revision operator is equivalent to the standard method for computing consistencybased diagnosis. We show how a diagnosis problem can be translated into a problem of belief revision and show how kernel constructions for revision operators can be used for computing diagnosis. We also show how Reiter's algorithm for computing diagnosis can be adapted for being used in belief revision. 1 Introduction Belief revision (for an overview, see [ Gardenfors, 1988; Gardenfors and Rott, 1995 ] ) deals with the problem of how to accommodate new assertions into an existent body of knowledge. Traditionally, the body of knowledge is represented by a belief set, a set of formulas closed under logical implication. Instead of belief sets we are going to use belief bases to represent belief states. A belief base is a set not closed under logical consequence [ Fuhrmann, 1991; Hansson, 1989; Nebel, 1992 ] . For every belief base B...
Belief Base Revision For Expressive Description Logics
 In Proc. of Workshop on OWL Experiences and Directions
, 2006
"... Abstract. In this work, we address the problem of revision of OWLDL knowledge bases. We focus on belief bases revision as it has previously been shown that OWLDL is not AGMcompliant for revision. Previously an algorithm for belief base semirevision for propositional logic has been defined; in pa ..."
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Cited by 24 (4 self)
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Abstract. In this work, we address the problem of revision of OWLDL knowledge bases. We focus on belief bases revision as it has previously been shown that OWLDL is not AGMcompliant for revision. Previously an algorithm for belief base semirevision for propositional logic has been defined; in particular it has been shown how the diagnosis problem can be translated into a revision problem. In this work, we expand upon this work and detail an approach for performing belief base semirevision in the Description Logic SHOIN, which corresponds to the W3C standard Web Ontology Language OWLDL. We additionally, discuss various optimizations to make the approach more practical. 1