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22
Circumscription
, 1996
"... The idea of circumscription can be explained on a simple example. We would like to represent information about the locations of blocks in a blocks world, using the "default": ..."
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Cited by 322 (11 self)
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The idea of circumscription can be explained on a simple example. We would like to represent information about the locations of blocks in a blocks world, using the &quot;default&quot;:
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.
On the Complexity of Propositional Knowledge Base Revision, Updates, and Counterfactuals
 ARTIFICIAL INTELLIGENCE
, 1992
"... We study the complexity of several recently proposed methods for updating or revising propositional knowledge bases. In particular, we derive complexity results for the following problem: given a knowledge base T , an update p, and a formula q, decide whether q is derivable from T p, the updated (or ..."
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Cited by 187 (12 self)
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We study the complexity of several recently proposed methods for updating or revising propositional knowledge bases. In particular, we derive complexity results for the following problem: given a knowledge base T , an update p, and a formula q, decide whether q is derivable from T p, the updated (or revised) knowledge base. This problem amounts to evaluating the counterfactual p > q over T . Besides the general case, also subcases are considered, in particular where T is a conjunction of Horn clauses, or where the size of p is bounded by a constant.
On the Computational Cost of Disjunctive Logic Programming: Propositional Case
, 1995
"... This paper addresses complexity issues for important problems arising with disjunctive logic programming. In particular, the complexity of deciding whether a disjunctive logic program is consistent is investigated for a variety of wellknown semantics, as well as the complexity of deciding whethe ..."
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Cited by 115 (26 self)
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This paper addresses complexity issues for important problems arising with disjunctive logic programming. In particular, the complexity of deciding whether a disjunctive logic program is consistent is investigated for a variety of wellknown semantics, as well as the complexity of deciding whether a propositional formula is satised by all models according to a given semantics. We concentrate on nite propositional disjunctive programs with as wells as without integrity constraints, i.e., clauses with empty heads; the problems are located in appropriate slots of the polynomial hierarchy. In particular, we show that the consistency check is P 2 complete for the disjunctive stable model semantics (in the total as well as partial version), the iterated closed world assumption, and the perfect model semantics, and we show that the inference problem for these semantics is P 2 complete; analogous results are derived for the an
Propositional Circumscription and Extended Closed World Reasoning are $\Pi^P_2$complete
 Theoretical Computer Science
, 1993
"... Circumscription and the closed world assumption with its variants are wellknown nonmonotonic techniques for reasoning with incomplete knowledge. Their complexity in the propositional case has been studied in detail for fragments of propositional logic. One open problem is whether the deduction prob ..."
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Cited by 99 (22 self)
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Circumscription and the closed world assumption with its variants are wellknown nonmonotonic techniques for reasoning with incomplete knowledge. Their complexity in the propositional case has been studied in detail for fragments of propositional logic. One open problem is whether the deduction problem for arbitrary propositional theories under the extended closed world assumption or under circumscription is $\Pi^P_2$complete, i.e., complete for a class of the second level of the polynomial hierarchy. We answer this question by proving these problems $\Pi^P_2$complete, and we show how this result applies to other variants of closed world reasoning.
A Survey on Complexity Results for Nonmonotonic Logics
 Journal of Logic Programming
, 1993
"... This paper surveys the main results appeared in the literature on the computational complexity of nonmonotonic inference tasks. We not only give results about the tractability/intractability of the individual problems but we also analyze sources of complexity and explain intuitively the nature of e ..."
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Cited by 82 (5 self)
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This paper surveys the main results appeared in the literature on the computational complexity of nonmonotonic inference tasks. We not only give results about the tractability/intractability of the individual problems but we also analyze sources of complexity and explain intuitively the nature of easy/hard cases. We focus mainly on nonmonotonic formalisms, like default logic, autoepistemic logic, circumscription, closedworld reasoning and abduction, whose relations with logic programming are clear and well studied. Complexity as well as recursiontheoretic results are surveyed. Work partially supported by the ESPRIT Basic Research Action COMPULOG and the Progetto Finalizzato Informatica of the CNR (Italian Research Council). The first author is supported by a CNR scholarship 1 Introduction Nonmonotonic logics and negation as failure in logic programming have been defined with the goal of providing formal tools for the representation of default information. One of the ideas und...
Is Intractability of NonMonotonic Reasoning a Real Drawback?
 Artificial Intelligence
, 1996
"... Several studies about computational complexity of nonmonotonic reasoning (NMR) showed that nonmonotonic inference is significantly harder than classical, monotonic inference. This contrasts with the general idea that NMR can be used to make knowledge representation and reasoning simpler, not harde ..."
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Cited by 43 (8 self)
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Several studies about computational complexity of nonmonotonic reasoning (NMR) showed that nonmonotonic inference is significantly harder than classical, monotonic inference. This contrasts with the general idea that NMR can be used to make knowledge representation and reasoning simpler, not harder. In this paper we show that, to some extent, NMR fulfills the representation goal. In particular, we prove that nonmonotonic formalisms such as circumscription and default logic allow for a much more compact and natural representation of propositional knowledge than propositional calculus. Proofs are based on a suitable definition of compilable inference problem, and on nonuniform complexity classes. Some results about intractability of circumscription and default logic can therefore be interpreted as the price one has to pay for having such an extracompact representation. On the other hand, intractability of inference and compactness of representation are not equivalent notions: we ex...
Logic Programming and Reasoning with Incomplete Information
 Annals of Mathematics and Artificial Intelligence
, 1994
"... The purpose of this paper is to expand the syntax and semantics of logic programs and disjunctive databases to allow for the correct representation of incomplete information in the presence of multiple extensions. The language of logic programs with classical negation, epistemic disjunction, and neg ..."
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Cited by 36 (4 self)
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The purpose of this paper is to expand the syntax and semantics of logic programs and disjunctive databases to allow for the correct representation of incomplete information in the presence of multiple extensions. The language of logic programs with classical negation, epistemic disjunction, and negation by failure is further expanded by new modal operators K and M (where for the set of rules T and formula F , KF stands for "F is known to be true by a reasoner with a set of premises T " and MF means " F may be believed to be true" by the same reasoner). Sets of rules in the extended language will be called epistemic specifications. We will define the semantics of epistemic specifications (which expands the semantics of disjunctive databases from [GL91]) and demonstrate their applicability to formalization of various forms of commonsense reasoning. In particular, we suggest a new formalization of the closed world assumption which seems to better correspond to the assumption's intuitive...
Complexity Aspects of Various Semantics for Disjunctive Databases
 In Proc. of the Twelfth ACM SIGACTSIGMODSIGART Symposium on Principles of Database Systems (PODS'93
, 1993
"... This paper addresses complexity issues for important problems arising with disjunctive databases. In particular, the complexity of inference of a literal and a formula from a propositional disjunctive database under a variety of wellknown disjunctive database semantics is investigated, as well decid ..."
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Cited by 25 (2 self)
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This paper addresses complexity issues for important problems arising with disjunctive databases. In particular, the complexity of inference of a literal and a formula from a propositional disjunctive database under a variety of wellknown disjunctive database semantics is investigated, as well deciding whether a disjunctive database has as model under a particular semantics. The problems are located in appropriate slots of the polynomial hierarchy. 1 Introduction Allowing to store disjunctions in a logical database is indispensable for dealing with disjunctive information. Accordingly, the meaning of a disjunctive database is expressed by a set of models instead of a single model as in case of nondisjunctive databases. A variety of different semantics for disjunctive databases has been proposed in the literature; see [9] for a comprehensive overview. We will deal with the following ones. ffl The Generalized Closed World Assumption (GCWA) by Minker [16]. ffl The Extended Generalized...
Specifying Closed World Assumptions for Logic Databases
 2nd Symp. on Mathematical Fundamentals of Database Syst. (MFDBS'89), 6884, LNCS 364
, 1989
"... "Closed world assumptions" (CWAs) are an important class of implicit completions for logic databases. We present a new general definition of CWA; it is parameterized, so that known and new versions of CWAs can be derived as special cases. Our CWA, in turn, instantiates the more basic notio ..."
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Cited by 24 (21 self)
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"Closed world assumptions" (CWAs) are an important class of implicit completions for logic databases. We present a new general definition of CWA; it is parameterized, so that known and new versions of CWAs can be derived as special cases. Our CWA, in turn, instantiates the more basic notion of "database completion" and satisfies natural properties. It can even be characterized by the property of determining maximal completions without generating too much new information. We study syntactic as well as semantic definitions and prove them to be equivalent. By discussing several instances of CWAs we demonstrate the applicability of our framework to database specification. 1 Introduction A logic database stores formulae which describe facts corresponding to conventional database information, rules for deducing further information, and indefinite information. Thus, a database state is a set of formulae and answers to queries should be logical consequences of such a state. The formulae are u...