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18
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 91 (6 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...
Knowledge Representation with Logic Programs
 DEPT. OF CS OF THE UNIVERSITY OF KOBLENZLANDAU
, 1996
"... In this tutorialoverview, which resulted from a lecture course given by the authors at ..."
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Cited by 38 (6 self)
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In this tutorialoverview, which resulted from a lecture course given by the authors at
Reducing Belief Revision to Circumscription (and viceversa)
, 2002
"... Nonmonotonic formalisms and belief revision operators have been introduced as useful tools to describe and reason about evolving scenarios. Both approaches have been proven effective in a number of different situations. However, little is known about their relationship. Previous work by Winslett ha ..."
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Cited by 22 (4 self)
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Nonmonotonic formalisms and belief revision operators have been introduced as useful tools to describe and reason about evolving scenarios. Both approaches have been proven effective in a number of different situations. However, little is known about their relationship. Previous work by Winslett has shown some correlations between a specific operator and circumscription. In this paper we greatly extend Winslett’s work by establishing new relations between circumscription and a large number of belief revision operators. This highlights similarities and differences between these formalisms. Furthermore, these connections provide us with the possibility of importing results in one field into the other one.
Capturing Parallel Circumscription with Disjunctive Logic Programs
 SpringerVerlag (2004) 134–146 LNAI 3229
, 2004
"... The stable model semantics of disjunctive logic programs is based on classical models which are minimal with respect to subset inclusion. As a consequence, every atom appearing in a disjunctive program is false by default. This is sometimes undesirable from the knowledge representation point of view ..."
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Cited by 17 (6 self)
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The stable model semantics of disjunctive logic programs is based on classical models which are minimal with respect to subset inclusion. As a consequence, every atom appearing in a disjunctive program is false by default. This is sometimes undesirable from the knowledge representation point of view and a more refined control of minimization is called for. Such features are already present in Lifschitz's parallel circumscription where certain atoms are allowed to vary or to have fixed values while all other atoms are minimized. In this paper, it is formally shown that the expressive power of minimal models is properly increased in the presence of varying atoms. In spite of this, we show how parallel circumscription can be embedded into disjunctive logic programming in a relatively systematic fashion using a linear and faithful, but nonmodular translation. This enables the conscious use of varying atoms in disjunctive logic programs leading to more elegant and concise problem representations in various domains.
Embedding Circumscriptive Theories in General Disjunctive Programs
 In Proceedings of the 3rd International Conference on Logic Programming and Nonmonotonic Reasoning
, 1995
"... . This paper presents a method of embedding circumscriptive theories in general disjunctive programs. In a general disjunctive program, negation as failure occurs not only in the body but in the head of a rule. In this setting, minimized predicates of a circumscriptive theory are specified using the ..."
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Cited by 12 (1 self)
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. This paper presents a method of embedding circumscriptive theories in general disjunctive programs. In a general disjunctive program, negation as failure occurs not only in the body but in the head of a rule. In this setting, minimized predicates of a circumscriptive theory are specified using the negation in the body, while fixed and varying predicates are expressed by the negation in the head. Moreover, the translation implies a close relationship between circumscription and abductive logic programming. That is, fixed and varying predicates in a circumscriptive theory are also viewed as abducible predicates in an abductive disjunctive program. Our method of translating circumscription into logic programming is fairly general compared with the existing approaches and exploits new applications of logic programming for representing commonsense knowledge. 1 Introduction It is wellknown that logic programming semantics have close relationships to circumscription. In early studies, Rei...
ObjectOriented FirstOrder Logic
 In Linkoping University Electronic Articles in Computer and Information Science, ISSN 1401–9841
, 2001
"... FirstOrder Logic (FOL) provides richness of representation, but is unwieldy in modeling large, complex tasks. On the other hand, the ObjectOriented paradigm has been successful in treating large, complex tasks in both software and knowledge engineering. This paper describes a novel logic that exte ..."
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Cited by 11 (4 self)
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FirstOrder Logic (FOL) provides richness of representation, but is unwieldy in modeling large, complex tasks. On the other hand, the ObjectOriented paradigm has been successful in treating large, complex tasks in both software and knowledge engineering. This paper describes a novel logic that extends FOL to create counterparts of the ObjectOriented paradigm. We call this logic ObjectOriented FirstOrder Logic (OOFOL). In this logic, objects are theories that are connected via interface vocabularies to other objects, classes are used to provide a reusable logical template, and inheritance is used to adapt classes to specialized tasks. We show that such a logic can be given simple semantics using FOL. A variant of the logic that allows some links between the objects to be unidirectional is also examined. This variant is called Directed ObjectOriented FirstOrder Logic (Directed OOFOL). It is shown that such a system can be given semantics using the nonmonotonic method of Circumscript...
Defeasible inclusions in lowcomplexity DLs
 JAIR
"... Some of the applications of OWL and RDF (e.g. biomedical knowledge representation and semantic policy formulation) call for extensions of these languages with nonmonotonic constructs such as inheritance with overriding. Nonmonotonic description logics have been studied for many years, however no pra ..."
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Cited by 10 (1 self)
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Some of the applications of OWL and RDF (e.g. biomedical knowledge representation and semantic policy formulation) call for extensions of these languages with nonmonotonic constructs such as inheritance with overriding. Nonmonotonic description logics have been studied for many years, however no practical such knowledge representation languages exist, due to a combination of semantic difficulties and high computational complexity. Independently, lowcomplexity description logics such as DLlite and EL have been introduced and incorporated in the OWL standard. Therefore, it is interesting to see whether the syntactic restrictions characterizing DLlite and EL bring computational benefits to their nonmonotonic versions, too. In this paper we extensively investigate the computational complexity of Circumscription when knowledge bases are formulated in DLliteR, EL, and fragments thereof. We identify fragments whose complexity ranges from P to the second level of the polynomial hierarchy, as well as fragments whose complexity raises to PSPACE and beyond. 1.
Formalising the Common Sense of a Mobile Robot
, 1998
"... Looking at the history of Artificial Intelligence, often theoretical rigor seems inversely proportional to practical applicability. Particularly, in the field of robotics, there is a gap between the research on knowledge representation and practical robotics. ..."
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Cited by 4 (3 self)
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Looking at the history of Artificial Intelligence, often theoretical rigor seems inversely proportional to practical applicability. Particularly, in the field of robotics, there is a gap between the research on knowledge representation and practical robotics.
Implementing Prioritized Circumscription by Computing Disjunctive Stable Models
, 2008
"... The stable model semantics of disjunctive logic programs is based on minimal models which assign atoms false by default. While this feature is highly useful and leads to concise problem encodings, it occasionally makes knowledge representation with disjunctive rules difficult. Lifschitz’ parallel ci ..."
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Cited by 3 (1 self)
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The stable model semantics of disjunctive logic programs is based on minimal models which assign atoms false by default. While this feature is highly useful and leads to concise problem encodings, it occasionally makes knowledge representation with disjunctive rules difficult. Lifschitz’ parallel circumscription provides a remedy by introducing atoms that are allowed to vary or to have fixed values while others are falsified. Prioritized circumscription further refines this setting in terms of priority classes for atoms being falsified. In this paper, we present a linear and faithful transformation to embed prioritized circumscription into disjunctive logic programming in a systematic fashion. The implementation of the method enables the use of disjunctive solvers for computing prioritized circumscription. The results of an experimental evaluation indicate that the method proposed herein compares favorably with other existing implementations.
Complexity of Nested Circumscription and Nested Abnormality Theories
, 2002
"... Circumscription has been recognized as an important principle for knowledge representation and commonsense reasoning. The need for a circumscriptive formalism that allows for simple yet elegant modular problem representation has led Lifschitz (AIJ, 1995) to introduce nested abnormality theories ..."
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Cited by 2 (1 self)
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Circumscription has been recognized as an important principle for knowledge representation and commonsense reasoning. The need for a circumscriptive formalism that allows for simple yet elegant modular problem representation has led Lifschitz (AIJ, 1995) to introduce nested abnormality theories (NATs) as a tool for modular knowledge representation, tailored for applying circumscription to minimize exceptional circumstances. Abstracting from this particular objective, we propose L CIRC , which is an extension of generic propositional circumscription by allowing propositional combinations and nesting of circumscriptive theories. As shown, NATs are naturally embedded into this language, and are in fact of equal expressive capability. We then analyze the complexity of L CIRC and NATs, and in particular the effect of nesting. The latter is found to be a source of complexity, which climbs the Polynomial Hierarchy as the nesting depth increases and reaches PSPACEcompleteness in the general case. We also identify meaningful syntactic fragments of NATs which have lower complexity. In particular, we show that the generalization of Horn circumscription in the NAT framework remains coNPcomplete, and that Horn NATs without fixed letters can be efficiently transformed into an equivalent Horn CNF, which implies polynomial solvability of principal reasoning tasks. Finally, we also study extensions of NATs and briefly address the complexity in the firstorder case. Our results give insight into the "cost" of using L CIRC (resp.