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181
Complexity and Expressive Power of Logic Programming
, 1997
"... This paper surveys various complexity results on different forms of logic programming. The main focus is on decidable forms of logic programming, in particular, propositional logic programming and datalog, but we also mention general logic programming with function symbols. Next to classical results ..."
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Cited by 287 (57 self)
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This paper surveys various complexity results on different forms of logic programming. The main focus is on decidable forms of logic programming, in particular, propositional logic programming and datalog, but we also mention general logic programming with function symbols. Next to classical results on plain logic programming (pure Horn clause programs), more recent results on various important extensions of logic programming are surveyed. These include logic programming with different forms of negation, disjunctive logic programming, logic programming with equality, and constraint logic programming. The complexity of the unification problem is also addressed.
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 227 (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.
The Complexity of LogicBased Abduction
, 1993
"... Abduction is an important form of nonmonotonic reasoning allowing one to find explanations for certain symptoms or manifestations. When the application domain is described by a logical theory, we speak about logicbased abduction. Candidates for abductive explanations are usually subjected to minima ..."
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Cited by 162 (26 self)
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Abduction is an important form of nonmonotonic reasoning allowing one to find explanations for certain symptoms or manifestations. When the application domain is described by a logical theory, we speak about logicbased abduction. Candidates for abductive explanations are usually subjected to minimality criteria such as subsetminimality, minimal cardinality, minimal weight, or minimality under prioritization of individual hypotheses. This paper presents a comprehensive complexity analysis of relevant decision and search problems related to abduction on propositional theories. Our results indicate that abduction is harder than deduction. In particular, we show that with the most basic forms of abduction the relevant decision problems are complete for complexity classes at the second level of the polynomial hierarchy, while the use of prioritization raises the complexity to the third level in certain cases.
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
A Survey on Knowledge Compilation
, 1998
"... this paper we survey recent results in knowledge compilation of propositional knowledge bases. We first define and limit the scope of such a technique, then we survey exact and approximate knowledge compilation methods. We include a discussion of compilation for nonmonotonic knowledge bases. Keywor ..."
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Cited by 97 (3 self)
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this paper we survey recent results in knowledge compilation of propositional knowledge bases. We first define and limit the scope of such a technique, then we survey exact and approximate knowledge compilation methods. We include a discussion of compilation for nonmonotonic knowledge bases. Keywords: Knowledge Representation, Efficiency of 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...
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 73 (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
Propositional Defeasible Logic has Linear Complexity
 of Logic Programming
, 2001
"... Defeasible logic is a rulebased nonmonotonic logic, with both strict and defeasible rules, and a priority relation on rules. We show that inference in the propositional form of the logic can be performed in linear time. This contrasts markedly with most other propositional nonmonotonic logics, i ..."
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Cited by 73 (6 self)
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Defeasible logic is a rulebased nonmonotonic logic, with both strict and defeasible rules, and a priority relation on rules. We show that inference in the propositional form of the logic can be performed in linear time. This contrasts markedly with most other propositional nonmonotonic logics, in which inference is intractable. 1 Introduction Mostwork in nonmonotonicreasoning has focussed on languages for whichpropositional inference is not tractable. Sceptical default reasoning is \Pi p 2 hard, even for very simple classes of default rules, as is sceptical autoepistemic reasoning and propositional circumscription. The complexity of sceptical inference from logic programs with negationasfailure varies according to the semantics of negation. For both the stable model semantics and the Clark completion, sceptical inference is coNPhard. See [13, 9] for more details. Although such languages are very expressive, and this expressiveness has been exploited in answerset progra...
A Declarative Approach to Business Rules in Contracts: Courteous Logic Programs in XML
, 1999
"... We address why, and especially how, to represent business rules in ecommerce contracts. By contracts, we mean descriptions of goods and services offered or sought, including ancillary agreements detailing terms of a deal. We observe that rules are useful in contracts to represent conditional r ..."
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Cited by 71 (4 self)
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We address why, and especially how, to represent business rules in ecommerce contracts. By contracts, we mean descriptions of goods and services offered or sought, including ancillary agreements detailing terms of a deal. We observe that rules are useful in contracts to represent conditional relationships, e.g., in terms & conditions, service provisions, and surrounding business processes, and we illustrate this point with several examples. We analyze requirements (desiderata) for representing such rules in contracts. The requirements include: declarative semantics so as to enable shared understanding and interoperability; prioritized conflict handling so as to enable modular updating/revision; ease of parsing; integration into WWWworld software engineering; direct executability; and computational tractability. We give a representational approach that consists of two novel aspects. First, we give a new fundamental knowledge representation formalism: a generalized ...