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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...
Stationary Semantics for Normal and Disjunctive Logic Programs
 Annals of Mathematics and Artificial Intelligence
, 1991
"... this paper we show, however, that stationary expansions can be equivalently defined in terms of classical, 2valued logic. As a byproduct, we obtain a simpler and more natural description of stationary expansions. ..."
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Cited by 71 (14 self)
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this paper we show, however, that stationary expansions can be equivalently defined in terms of classical, 2valued logic. As a byproduct, we obtain a simpler and more natural description of stationary expansions.
Solving Advanced Reasoning Tasks using Quantified Boolean Formulas
, 2000
"... We consider the compilation of different reasoning tasks into the evaluation problem of quantified boolean formulas (QBFs) as an approach to develop prototype reasoning systems useful, e.g., for experimental purposes. ..."
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Cited by 68 (20 self)
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We consider the compilation of different reasoning tasks into the evaluation problem of quantified boolean formulas (QBFs) as an approach to develop prototype reasoning systems useful, e.g., for experimental purposes.
Stationary Default Extensions
 Fundamenta Informaticae
, 1992
"... this paper we introduce the class of so called stationary extensions of a default theory. Stationary extensions include, as a special case, Reiter's original default extensions but allow us to eliminate their drawbacks that were mentioned above. Every default theory \Delta has at least one stationar ..."
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Cited by 24 (0 self)
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this paper we introduce the class of so called stationary extensions of a default theory. Stationary extensions include, as a special case, Reiter's original default extensions but allow us to eliminate their drawbacks that were mentioned above. Every default theory \Delta has at least one stationary extension and among its extensions there always exists the least stationary extension E \Delta . The (cautious) stationary semantics S (\Delta) of a default theory \Delta, i.e., the theory consisting of sentences which are true in all stationary extensions of \Delta, is always welldefined, and, since it clearly coincides with the least stationary extension E \Delta of \Delta, it is itself a stationary extension of \Delta. The stationary semantics of default theories is always cumulatively monotonic and it can be computed by means of a natural iterative procedure. The complexity of its computation essentially coincides with the computational complexity of satisfiability tests on the underlying first order theory and therefore it does not involve any additional complexity caused by the nonmonotonicity of default logic. More precisely, for default theories consisting of
Semantics and complexity of abduction from default theories
 Artificial Intelligence
, 1997
"... Since logical knowledge representation is commonly based on nonclassical formalisms like default logic, autoepistemic logic, or circumscription, it is necessary to perform abductive reasoning from theories of nonclassical logics. In this paper, we investigate how abduction can be performed from theo ..."
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Cited by 21 (2 self)
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Since logical knowledge representation is commonly based on nonclassical formalisms like default logic, autoepistemic logic, or circumscription, it is necessary to perform abductive reasoning from theories of nonclassical logics. In this paper, we investigate how abduction can be performed from theories in default logic. Different modes of abduction are plausible, based on credulous and skeptical default reasoning; they appear useful for different applications such as diagnosis and planning. Moreover, we analyze the complexity of the main abductive reasoning tasks. They are intractable in the general case; we also present known classes of default theories for which abduction is tractable. 1
Static Semantics as Program Transformation and Wellfounded Computation
 Nonmonotonic Extensions of Logic Programming, LNAI 927
, 1995
"... Abstract. In this paper, we propose a new constructive characterization of those semantics for disjunctive logic programs which are extensions of the wellfounded semantics for normal programs. Based on considerations about how disjunctive information is treated by a given semantics, we divide the c ..."
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Cited by 6 (0 self)
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Abstract. In this paper, we propose a new constructive characterization of those semantics for disjunctive logic programs which are extensions of the wellfounded semantics for normal programs. Based on considerations about how disjunctive information is treated by a given semantics, we divide the computation of that semantics into two phases. The first one is a program transformation phase, which applies axiom schemata expressing how derivations involving disjunctions are made in the given semantic framework. The second one is a constructive phase, based on a variation of the wellfounded model construction for normal programs. We apply this twophases procedural semantics to the computation of the static semantics of disjunctive logic programs as a casestudy, showing how it works and what its results are in several examples. A main perspective of this proposal is a procedural semantics for disjunctive programs consisting of an inefficient preprocessing phase (implementing the program transformation procedure), to be however performed only once, and of an efficient runtime computation, obtained as a variation of any effective procedural semantics for the wellfounded model. 1
Expressing Default Abduction Problems as Quantified Boolean Formulas
 AI Communications
, 2002
"... Abduction is the process of finding explanations for observed phenomena in accord to known laws about a given application domain. This form of reasoning is an important principle of commonsense reasoning and is particularly relevant in conjunction with nonmonotonic knowledge representation formalis ..."
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Cited by 4 (3 self)
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Abduction is the process of finding explanations for observed phenomena in accord to known laws about a given application domain. This form of reasoning is an important principle of commonsense reasoning and is particularly relevant in conjunction with nonmonotonic knowledge representation formalisms. In this paper, we deal with a model for abduction in which the domain knowledge is represented in terms of a default theory. We show how the main reasoning tasks associated with this particular form of abduction can be axiomatised within the language of quantified Boolean logic. More specifically, we provide polynomialtime constructible reductions mapping a given abduction problem into a quantified Boolean formula (QBF) such that the satisfying truth assignments to the free variables of the latter determine the solutions of the original problem. Since there are now efficient QBFsolvers available, this reduction technique yields a straightforward method to implement the discussed abduction tasks. We describe a realisation of this approach by appeal to the reasoning system QUIP.