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123
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 281 (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 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.
An Algorithm to Evaluate Quantified Boolean Formulae and its Experimental Evaluation
 Journal of Automated Reasoning
, 1999
"... The high computational complexity of advanced reasoning tasks such as reasoning about knowledge and planning calls for efficient and reliable algorithms for reasoning problems harder than NP. In this paper we propose Evaluate, an algorithm for evaluating Quantified Boolean Formulae, a language that ..."
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Cited by 141 (2 self)
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The high computational complexity of advanced reasoning tasks such as reasoning about knowledge and planning calls for efficient and reliable algorithms for reasoning problems harder than NP. In this paper we propose Evaluate, an algorithm for evaluating Quantified Boolean Formulae, a language that extends propositional logic in a way such that many advanced forms of propositional reasoning, e.g., circumscription, can be easily formulated as evaluation of a QBF. Algorithms for evaluation of QBFs are suitable for the experimental analysis on a wide range of complexity classes, a property not easily found in other formalisms. Evaluate is based on a generalization of the DavisPutnam procedure for SAT, and is guaranteed to work in polynomial space. Before presenting the algorithm, we discuss several abstract properties of QBFs that we singled out to make it more efficient. We also discuss various options that were investigated about heuristics and data structures, and report the main res...
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 to de ..."
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Cited by 132 (17 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
A Deductive System for NonMonotonic Reasoning
, 1997
"... Disjunctive Deductive Databases (DDDBs)  functionfree disjunctive logic programs with negation in rule bodies allowed  have been recently recognized as a powerful tool for knowledge representation and commonsense reasoning. Much research has been spent on issues like semantics and complexity ..."
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Cited by 104 (21 self)
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Disjunctive Deductive Databases (DDDBs)  functionfree disjunctive logic programs with negation in rule bodies allowed  have been recently recognized as a powerful tool for knowledge representation and commonsense reasoning. Much research has been spent on issues like semantics and complexity of DDDBs, but the important area of implementing DDDBs has been less addressed so far. However, a thorough investigation thereof is a basic requirement for building systems which render previous foundational work on DDDBs useful for practice. This paper presents the architecture of a DDDB system currently developed at TU Vienna in the FWF project P11580MAT "A Query System for Disjunctive Deductive Databases".
Tractable Reasoning via Approximation
 Artificial Intelligence
, 1995
"... Problems in logic are wellknown to be hard to solve in the worst case. Two different strategies for dealing with this aspect are known from the literature: language restriction and theory approximation. In this paper we are concerned with the second strategy. Our main goal is to define a semantical ..."
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Cited by 92 (0 self)
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Problems in logic are wellknown to be hard to solve in the worst case. Two different strategies for dealing with this aspect are known from the literature: language restriction and theory approximation. In this paper we are concerned with the second strategy. Our main goal is to define a semantically wellfounded logic for approximate reasoning, which is justifiable from the intuitive point of view, and to provide fast algorithms for dealing with it even when using expressive languages. We also want our logic to be useful to perform approximate reasoning in different contexts. We define a method for the approximation of decision reasoning problems based on multivalued logics. Our work expands and generalizes in several directions ideas presented by other researchers. The major features of our technique are: 1) approximate answers give semantically clear information about the problem at hand; 2) approximate answers are easier to compute than answers to the original problem; 3) approxim...
Compositional Shape Analysis by means of BiAbduction
, 2009
"... This paper describes a compositional shape analysis, where each procedure is analyzed independently of its callers. The analysis uses an abstract domain based on a restricted fragment of separation logic, and assigns a collection of Hoare triples to each procedure; the triples provide an overapprox ..."
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Cited by 87 (16 self)
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This paper describes a compositional shape analysis, where each procedure is analyzed independently of its callers. The analysis uses an abstract domain based on a restricted fragment of separation logic, and assigns a collection of Hoare triples to each procedure; the triples provide an overapproximation of data structure usage. Compositionality brings its usual benefits – increased potential to scale, ability to deal with unknown calling contexts, graceful way to deal with imprecision – to shape analysis, for the first time. The analysis rests on a generalized form of abduction (inference of explanatory hypotheses) which we call biabduction. Biabduction displays abduction as a kind of inverse to the frame problem: it jointly infers antiframes (missing portions of state) and frames (portions of state not touched by an operation), and is the basis of a new interprocedural analysis algorithm. We have implemented
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...
Representing and reasoning about semantic conflicts in heterogeneous information systems
, 1997
"... ..."
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 74 (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