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193
Improvements to the evaluation of quantified Boolean formulae
 In Proceedings of the Sixteenth International Joint Conference on Artificial Intelligence (IJCAI'99), July 31August 6
, 1999
"... We present a theoremprover for quantified Boolean formulae and evaluate it on random quantified formulae and formulae that represent problems from automated planning. Even though the notion of quantified Boolean formula is theoretically important, automated reasoning with QBF has not been thoroughl ..."
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Cited by 76 (3 self)
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We present a theoremprover for quantified Boolean formulae and evaluate it on random quantified formulae and formulae that represent problems from automated planning. Even though the notion of quantified Boolean formula is theoretically important, automated reasoning with QBF has not been thoroughly investigated. Universal quantifiers are needed in representing many computational problems that cannot be easily translated to the propositional logic and solved by satisfiability algorithms. Therefore efficient reasoning with QBF is important. The DavisPutnam procedure can be extended to evaluate quantified Boolean formulae. A straightforward algorithm of this kind is not very efficient. We identify universal quantifiers as the main area where improvements to the basic algorithm can be made. We present a number of techniques for reducing the amount of search that is needed, and evaluate their effectiveness by running the algorithm on a collection of formulae obtained from planning and generated randomly. For the structured problems we consider, the techniques lead to a dramatic speedup. 1
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 59 (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
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 (17 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.
Prioritized Logic Programming and Its Application to Commonsense Reasoning
, 2000
"... Representing and reasoning with priorities are important in commonsense reasoning. This paper introduces a framework of prioritized logic programming (PLP), which has a mechanism of explicit representation of priority information in a program. When a program contains incomplete or indefinite informa ..."
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Cited by 53 (1 self)
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Representing and reasoning with priorities are important in commonsense reasoning. This paper introduces a framework of prioritized logic programming (PLP), which has a mechanism of explicit representation of priority information in a program. When a program contains incomplete or indefinite information, PLP is useful for specifying preference to reduce nondeterminism in logic programming. Moreover, PLP can realize various forms of commonsense reasoning in AI such as abduction, default reasoning, circumscription, and their prioritized variants. The proposed framework increases the expressive power of logic programming and exploits new applications in knowledge representation. Keywords: prioritized logic programs, abduction, default reasoning, prioritized circumscription 1 Introduction In commonsense reasoning a theory is usually assumed incomplete and may contain indefinite or conflicting knowledge. Under such circumstances, priority information is useful to select appropriate know...
Abductive matchmaking using description logics
 In Proc. of IJCAI 2003
, 2003
"... Motivated by the matchmaking problem in electronic marketplaces, we study abduction in Description Logics. We devise suitable definitions of the problem, and show how they can model commonsense reasoning usually employed in analyzing classified announcements having a standardized terminology. We the ..."
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Cited by 52 (36 self)
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Motivated by the matchmaking problem in electronic marketplaces, we study abduction in Description Logics. We devise suitable definitions of the problem, and show how they can model commonsense reasoning usually employed in analyzing classified announcements having a standardized terminology. We then describe a system partially implementing these ideas, and present a simple experiment, which shows the correspondence between the system behavior with human users judgement.
Default Logic as a Query Language
, 1997
"...  Research in nonmonotonic reasoning has focused largely on the idea of representing knowledge about the world via rules that are generally true but can be defeated. Even if relational databases are nowadays the main tool for storing very large sets of data, the approach of using nonmonotonic AI f ..."
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Cited by 49 (11 self)
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 Research in nonmonotonic reasoning has focused largely on the idea of representing knowledge about the world via rules that are generally true but can be defeated. Even if relational databases are nowadays the main tool for storing very large sets of data, the approach of using nonmonotonic AI formalisms as relational database query languages has been investigated to a much smaller extent. In this work we propose a novel application of Reiter's default logic by introducing a default query language (DQL) for nite relational databases, which is based on default rules. The main result of this paper is that DQL is as expressive as SO 98 , the existentialuniversal fragment of secondorder logic. This result is not only of theoretical importance: We exhibit queries {which are useful in practice{ that can be expressed with DQL and can not with other query languages based on nonmonotonic logics such as DATALOG with negation under the stable model semantics. In particular, we show that DQ...
A case for abductive reasoning over ontologies.
 In Proceedings of OWL: Experiences and Directions.
, 2006
"... ..."
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
Bounded treewidth as a key to tractability of knowledge representation and reasoning
 IN PROCEEDINGS OF THE 21ST NATIONAL CONFERENCE ON ARTIFICIAL INTELLIGENCE (AAAI’06
, 2006
"... Several forms of reasoning in AI – like abduction, closed world reasoning, circumscription, and disjunctive logic programming – are well known to be intractable. In fact, many of the relevant problems are on the second or third level of the polynomial hierarchy. In this paper, we show how the powerf ..."
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Cited by 32 (16 self)
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Several forms of reasoning in AI – like abduction, closed world reasoning, circumscription, and disjunctive logic programming – are well known to be intractable. In fact, many of the relevant problems are on the second or third level of the polynomial hierarchy. In this paper, we show how the powerful notion of treewidth can be fruitfully applied to this area. In particular, we show that all these problems become tractable (actually, even solvable in linear time), if the treewidth of the involved formulae (or of the disjunctive logic programs, resp.) is bounded by some constant. Experiments with a prototype implementation prove the feasibility of this new approach, in principle, and also give us hints for necessary improvements. In many areas of computer science, bounded treewidth has been shown to be a realistic and practically relevant restriction. We thus argue that bounded treewidth is a key factor in the development of efficient algorithms also in knowledge representation and reasoning – despite the high worst case complexity of the problems of interest.