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48
Ultimate Wellfounded and Stable Semantics for Logic Programs With Aggregates (Extended Abstract)
 In Proceedings of ICLP01, LNCS 2237
, 2001
"... is relatively straightforward. Another advantage of the ultimate approximation is that in cases where TP is monotone the ultimate wellfounded model will be 2valued and will coincide with the least fixpoint of TP . This is not the case for the standard wellfounded semantics. For example in the sta ..."
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Cited by 63 (11 self)
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is relatively straightforward. Another advantage of the ultimate approximation is that in cases where TP is monotone the ultimate wellfounded model will be 2valued and will coincide with the least fixpoint of TP . This is not the case for the standard wellfounded semantics. For example in the standard wellfounded model of the program: # p. p. p is undefined while the associated TP operator is monotone and p is true in the ultimate wellfounded model. One disadvantage of using the ultimate semantics is that it has a higher computational cost even for programs without aggregates. The complexity goes one level higher in the polynomial hierarchy to # 2 for the wellfounded model and to 2 for a stable model which is also complete for this class [2]. Fortunately, by adding aggregates the complexity does not increase further. To give an example of a logic program with aggregates we consider the problem of computing the length of the shortest path between two nodes in a direc
A logic of nonmonotone inductive definitions
 ACM transactions on computational logic
, 2007
"... Wellknown principles of induction include monotone induction and different sorts of nonmonotone induction such as inflationary induction, induction over wellfounded sets and iterated induction. In this work, we define a logic formalizing induction over wellfounded sets and monotone and iterated i ..."
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Cited by 56 (36 self)
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Wellknown principles of induction include monotone induction and different sorts of nonmonotone induction such as inflationary induction, induction over wellfounded sets and iterated induction. In this work, we define a logic formalizing induction over wellfounded sets and monotone and iterated induction. Just as the principle of positive induction has been formalized in FO(LFP), and the principle of inflationary induction has been formalized in FO(IFP), this paper formalizes the principle of iterated induction in a new logic for NonMonotone Inductive Definitions (IDlogic). The semantics of the logic is strongly influenced by the wellfounded semantics of logic programming. This paper discusses the formalisation of different forms of (non)monotone induction by the wellfounded semantics and illustrates the use of the logic for formalizing mathematical and commonsense knowledge. To model different types of induction found in mathematics, we define several subclasses of definitions, and show that they are correctly formalized by the wellfounded semantics. We also present translations into classical first or second order logic. We develop modularity and totality results and demonstrate their use to analyze and simplify complex definitions. We illustrate the use of the logic for temporal reasoning. The logic formally extends Logic Programming, Abductive Logic Programming and Datalog, and thus formalizes the view on these formalisms as logics of (generalized) inductive definitions. Categories and Subject Descriptors:... [...]:... 1.
Non Monotonic Reasoning
, 1997
"... These are the proceedings of the 11th Nonmonotonic Reasoning Workshop. The aim of this series ..."
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Cited by 33 (1 self)
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These are the proceedings of the 11th Nonmonotonic Reasoning Workshop. The aim of this series
Embedding NonGround Logic Programs into Autoepistemic Logic for Knowledge Base Combination
, 2008
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Managing uncertainty and vagueness in description logics, logic Reducing Fuzzy Answer Set Programming to Model Finding in Fuzzy Logics 33 programs and description logic programs
 In Reasoning Web: 4th International Summer School 2008
"... Abstract. Managing uncertainty and/or vagueness is starting to play an important role in Semantic Web representation languages. Our aim is to overview basic concepts on representing uncertain and vague knowledge in current Semantic Web ontology and rule languages (and their combination). 1 ..."
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Cited by 23 (5 self)
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Abstract. Managing uncertainty and/or vagueness is starting to play an important role in Semantic Web representation languages. Our aim is to overview basic concepts on representing uncertain and vague knowledge in current Semantic Web ontology and rule languages (and their combination). 1
Approximations, Stable Operators, WellFounded Fixpoints And Applications In Nonmonotonic Reasoning
, 2000
"... In this paper we develop an algebraic framework for studying semantics of nonmonotonic logics. Our approach is formulated in the language of lattices, bilattices, operators and fixpoints. The goal is to describe fixpoints of an operator O defined on a lattice. The key intuition is that of an approxi ..."
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Cited by 23 (9 self)
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In this paper we develop an algebraic framework for studying semantics of nonmonotonic logics. Our approach is formulated in the language of lattices, bilattices, operators and fixpoints. The goal is to describe fixpoints of an operator O defined on a lattice. The key intuition is that of an approximation, a pair (x, y) of lattice elements which can be viewed as an approximation to each lattice element z such that x z y. The key notion is that of an approximating operator, a monotone operator on the bilattice of approximations whose fixpoints approximate the fixpoints of the operator O. The main contribution of the paper is an algebraic construction which assigns a certain operator, called the stable operator, to every approximating operator on a bilattice of approximations. This construction leads to an abstract version of the wellfounded semantics. In the paper we show that our theory offers a unified framework for semantic studies of logic programming, default logic and autoepistemic logic.
Logic programs with abstract constraint atoms: the role of computations
 Proceedings of the 23rd International Conference on Logic Programming (ICLP 2007), LNCS, Springer, 2007 (this
, 2005
"... Abstract. We provide new perspectives on the semantics of logic programs with constraints. To this end we introduce several notions of computation and propose to use the results of computations as answer sets of programs with constraints. We discuss the rationale behind different classes of computat ..."
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Cited by 22 (2 self)
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Abstract. We provide new perspectives on the semantics of logic programs with constraints. To this end we introduce several notions of computation and propose to use the results of computations as answer sets of programs with constraints. We discuss the rationale behind different classes of computations and study the relationships among them and among the corresponding concepts of answer sets. The proposed semantics generalize the answer set semantics for programs with monotone, convex and/or arbitrary constraints described in the literature. 1
Ultimate approximation and its application in nonmonotonic knowledge representation systems
, 2004
"... ..."
An epistemic foundation of stable model semantics
, 2003
"... The stable model semantics has become a dominating approach for the management of negation in logic programming. It relies mainly on the closed world assumption to complete the available knowledge and its formulation has its founding root in the socalled GelfondLifschitz transform. The primary goa ..."
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Cited by 13 (3 self)
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The stable model semantics has become a dominating approach for the management of negation in logic programming. It relies mainly on the closed world assumption to complete the available knowledge and its formulation has its founding root in the socalled GelfondLifschitz transform. The primary goal of this work is to present an alternative and epistemic based characterization of the stable model semantics, to the GelfondLifschitz transform. In particular, we show that the stable model semantics can be defined entirely as an extension of the KripkeKleene semantics and, thus, (i) does rely on the classical management of negation; and (ii) does not require any program transformation. Indeed, we show that the closed world assumption can be seen as an additional source for ‘falsehood ’ to be added cumulatively to the KripkeKleene semantics. Our approach is purely algebraic and can abstract from the particular formalism of choice as it is based on monotone operators (under the knowledge order) over bilattices only.
Embedding approaches to combining rules and ontologies into autoepistemic logic
 In Proc. 11th International Conference on Principles of Knowledge Representation and Reasoning (KR’08
"... The combination of rules and ontologies has a central role in the ongoing development of the Semantic Web. In previous work, autoepistemic logic (AEL) was advocated as a uniform host formalism to study different such combinations, enabling comparisons on a common basis. In this paper, we continue th ..."
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Cited by 12 (4 self)
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The combination of rules and ontologies has a central role in the ongoing development of the Semantic Web. In previous work, autoepistemic logic (AEL) was advocated as a uniform host formalism to study different such combinations, enabling comparisons on a common basis. In this paper, we continue this line of research and investigate different embeddings of major proposals to combine rules and ontologies into firstorder autoepistemic logic (FOAEL). In particular, we present embeddings for dlprograms, rhybrid knowledge bases, and hybrid MKNF knowledge bases, which are representatives of different combination types. We study the embeddings in the context of FOAEL under the standardnames assumption, but we also discuss variants using the any and allnames semantics. Our results provide interesting insights into the properties of the discussed combination formalisms.