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Logic Programming and Knowledge Representation
 Journal of Logic Programming
, 1994
"... In this paper, we review recent work aimed at the application of declarative logic programming to knowledge representation in artificial intelligence. We consider exten sions of the language of definite logic programs by classical (strong) negation, disjunc tion, and some modal operators and sh ..."
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Cited by 224 (21 self)
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In this paper, we review recent work aimed at the application of declarative logic programming to knowledge representation in artificial intelligence. We consider exten sions of the language of definite logic programs by classical (strong) negation, disjunc tion, and some modal operators and show how each of the added features extends the representational power of the language.
Embedding Defaults into Terminological Knowledge Representation Formalisms
 Journal of Automated Reasoning
, 1995
"... We consider the problem of integrating Reiter's default logic into terminological representation systems. It turns out that such an integration is less straightforward than we expected, considering the fact that the terminological language is a decidable sublanguage of firstorder logic. Semanticall ..."
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Cited by 125 (6 self)
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We consider the problem of integrating Reiter's default logic into terminological representation systems. It turns out that such an integration is less straightforward than we expected, considering the fact that the terminological language is a decidable sublanguage of firstorder logic. Semantically, one has the unpleasant effect that the consequences of a terminological default theory may be rather unintuitive, and may even vary with the syntactic structure of equivalent concept expressions. This is due to the unsatisfactory treatment of open defaults via Skolemization in Reiter's semantics. On the algorithmic side, we show that this treatment may lead to an undecidable default consequence relation, even though our base language is decidable, and we have only finitely many (open) defaults. Because of these problems, we then consider a restricted semantics for open defaults in our terminological default theories: default rules are only applied to individuals that are explicitly presen...
QuickXPlain: Conflict Detection for Arbitrary Constraint Propagation Algorithms
, 2001
"... Existing conflict detection methods for CSP's such as [de Kleer, 1989; Ginsberg, 1993] cannot make use of powerful propagation which makes them unusable for complex realworld problems. On the other hand, powerful constraint propagation methods lack the ability to extract dependencies or conflicts, ..."
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Cited by 70 (0 self)
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Existing conflict detection methods for CSP's such as [de Kleer, 1989; Ginsberg, 1993] cannot make use of powerful propagation which makes them unusable for complex realworld problems. On the other hand, powerful constraint propagation methods lack the ability to extract dependencies or conflicts, which makes them unusable for many advanced AI reasoning methods that require conflicts, as well as for interactive applications that require explanations. In this paper, we present a nonintrusive conflict detection algorithm called QUICKXPLAIN that tackles those problems. It can be applied to any propagation or inference algorithm as powerful as it may be. Our algorithm improves the efficiency of direct nonintrusive conflict detectors by recursively partitioning the problem into subproblems of half the size and by immediately skipping those subproblems that do not contain an element of the conflict. QUICKXPLAIN is used as explanation component of an advanced industrial constraintbased configuration tool.
Computing With Default Logic
, 1999
"... Default logic was proposed by Reiter as a knowledge representation tool. In this paper, we present our work on the Default Reasoning System, DeReS, the first comprehensive and optimized implementation of default logic. While knowledge representation remains the main application area for default l ..."
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Cited by 39 (5 self)
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Default logic was proposed by Reiter as a knowledge representation tool. In this paper, we present our work on the Default Reasoning System, DeReS, the first comprehensive and optimized implementation of default logic. While knowledge representation remains the main application area for default logic, as a source of largescale problems needed for experimentation and as a source of intuitions needed for a systematic methodology of encoding problems as default theories we use here the domain of combinatorial problems. To experimentally study the performance of DeReS we developed a benchmarking system, the TheoryBase. The TheoryBase is designed to support experimental investigations of nonmonotonic reasoning systems based on the language of default logic or logic programming. It allows the user to create parameterized collections of default theories having similar properties and growing sizes and, consequently, to study the asymptotic performance of nonmonotonic systems under i...
Experimenting with Nonmonotonic Reasoning
 IN PROCEEDINGS OF THE 12TH INTERNATIONAL CONFERENCE ON LOGIC PROGRAMMING
, 1995
"... In this paper, we describe a system, called TheoryBase, whose goal is to facilitate experimental studies of nonmonotonic reasoning systems. TheoryBase generates test default theories and logic programs. It has an identification system for generated theories, which allows us to reconstruct a logic pr ..."
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Cited by 37 (6 self)
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In this paper, we describe a system, called TheoryBase, whose goal is to facilitate experimental studies of nonmonotonic reasoning systems. TheoryBase generates test default theories and logic programs. It has an identification system for generated theories, which allows us to reconstruct a logic program or a default theory from its identifier. Hence, exchanging test cases requires only exchanging identifiers. TheoryBase can generate a large variety of examples of default theories and logic programs. We believe that its universal adoption may significantly advance experimental studies of nonmonotonic reasoning systems.
Computing intersection of autoepistemic expansions
 Proc. LPNMR91
, 1991
"... In this paper, we consider the question of skeptical reasoning for an important nonmonotonic reasoning system — the autoepistemic logic of Moore. Autoepistemic logic is a method of reasoning which assigns to a set of formulas the collection of theories called stable expansions. A naive method to per ..."
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Cited by 28 (1 self)
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In this paper, we consider the question of skeptical reasoning for an important nonmonotonic reasoning system — the autoepistemic logic of Moore. Autoepistemic logic is a method of reasoning which assigns to a set of formulas the collection of theories called stable expansions. A naive method to perform skeptical autoepistemic reasoning — deciding whether a given formula ϕ belongs to all expansions of a theory — is to compute first all expansions and then check whether ϕ belongs to each of them. This approach to skeptical autoepistemic reasoning is however prohibitively inefficient. The goal of this paper is to propose a different approach to computing intersection of all expansions of a theory. Our approach does not require us to compute any expansion of a theory. It reduces the question of membership in the intersection of all expansions to the question of propositional provability. More precisely, we describe a method that assigns to a modal theory I a propositional theory PI and to a modalfree formula ϕ another formula ϕ ′ in such a manner that ϕ is in the intersection of all expansions of I if and only if PI ⊢ ϕ ′. In general, the theory PI is much larger than the original theory I. We have found, however, several cases when it is not so and the size of the theory PI is a polynomial in the size of I. These classes of theories are closely related to logic programs and disjunctive logic programs. Consequently, we obtain methods to check whether an atom is in the intersection of all supported (or stable) models of a (disjunctive) logic program, as well as numerous complexity results. 1
Towards efficient default reasoning
 PROC. IJCAI95
, 1995
"... A decision method for Reiter's default logic is developed. It can determine whether a default theory has an extension, whether a formula is in some extension of a default theory and whether a formula is in every extension of a default theory. The method handles full propositional default logic. It c ..."
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Cited by 28 (4 self)
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A decision method for Reiter's default logic is developed. It can determine whether a default theory has an extension, whether a formula is in some extension of a default theory and whether a formula is in every extension of a default theory. The method handles full propositional default logic. It can be implemented to work in polynomial space and by using only a theorem prover for the underlying propositional logic as a subroutine. The method divides default reasoning into two major subtasks: the search task of examining every alternative for extensions, which is solved by backtracking search, and the classical reasoning task, which can be implemented by a theorem prover for the underlying classical logic. Special emphasis is given to the search problem. The decision method employs a new compact representation of extensions which reduces the search space. Efficient techniques for pruning the search space further are developed.
Default Reasoning Using Classical Logic
 Artificial Intelligence
, 1996
"... In this paper we show how propositional default theories can be characterized by classical propositional theories: for each finite default theory, we show a classical propositional theory such that there is a onetoone correspondence between models for the latter and extensions of the former. T ..."
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Cited by 22 (2 self)
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In this paper we show how propositional default theories can be characterized by classical propositional theories: for each finite default theory, we show a classical propositional theory such that there is a onetoone correspondence between models for the latter and extensions of the former. This means that computing extensions and answering queries about coherence, setmembership and setentailment are reducible to propositional satisfiability. The general transformation is exponential but tractable for a subset which we call 2DT  a superset of network default theories and disjunctionfree default theories. Consequently, coherence and setmembership for the class 2DT is NPcomplete and setentailment is coNPcomplete. This work paves the way for the application of decades of research on efficient algorithms for the satisfiability problem to default reasoning. For example, since propositional satisfiability can be regarded as a constraint satisfaction problem (CSP...
A decision method for nonmonotonic reasoning based on autoepistemic reasoning
 IN PROCEEDINGS OF THE 4TH INTERNATIONAL CONFERENCE ON PRINCIPLES OF KNOWLEDGE REPRESENTATION AND REASONING
, 1994
"... A novel decision method for autoepistemic reasoning is developed and proved correct. The method is applicable in a general setting, i.e. for an autoepistemic logic based on a given classical logic. It provides a decision procedure for a tightly grounded form of autoepistemic reasoning based on Lhier ..."
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Cited by 17 (4 self)
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A novel decision method for autoepistemic reasoning is developed and proved correct. The method is applicable in a general setting, i.e. for an autoepistemic logic based on a given classical logic. It provides a decision procedure for a tightly grounded form of autoepistemic reasoning based on Lhierarchic expansions as well as for autoepistemic reasoning based on Moore style expansions and Nexpansions. Prominent formalizations of nonmonotonic reasoning, such as default logic and circumscription, can be embedded into autoepistemic logic based on Lhierarchic expansions using simple local translations. Hence, the method can serve as a unified reasoning tool for a wide range of forms of nonmonotonic reasoning. The method is conceptually simple and the inherent sources of complexity and targets for optimization are clearly identifiable. As an example of exploiting optimization possibilities a new decision method for Reiter's default logic is developed where ideas from autoepistemic reasoning are used to efficiently prune the search space of applying default rules when constructing extensions of a default theory.
Evaluating an Algorithm for Default Reasoning
, 1995
"... In this paper performance of a lately proposed decision procedure for Reiter's default logic is evaluated. Recent complexity results indicate that there are two orthogonal sources of complexity in default reasoning: classical (firstorder) reasoning and conflict resolution (i.e. choosing an appropri ..."
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Cited by 13 (3 self)
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In this paper performance of a lately proposed decision procedure for Reiter's default logic is evaluated. Recent complexity results indicate that there are two orthogonal sources of complexity in default reasoning: classical (firstorder) reasoning and conflict resolution (i.e. choosing an appropriate set of applicable nonconflicting default rules). For classical reasoning wellknown techniques exist and conflict resolution presents the new computational challenge in default reasoning. However, efficient conflict resolution methods have been lacking. The recently introduced default reasoning algorithm pays special attention to conflict resolution and in this paper the efficiency of the conflict resolution technique in the new algorithm is examined. To rule out classical reasoning, a fragment of default logic with only atomic formulae is considered. This fragment corresponds to the stable model semantics of propositional logic programs. As an interesting test domain for nonmonotonic reas...