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12
Managing uncertainty and vagueness in description logics, logic programs and description logic programs
, 2008
"... 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). ..."
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Cited by 22 (6 self)
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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).
The Approximate Wellfounded Semantics for Logic Programs with Uncertainty
 In 28th International Symposium on Mathematical Foundations of Computer Science (MFCS2003), number 2747 in Lecture Notes in Computer Science
, 2003
"... The management of uncertain information in logic programs becomes to be important whenever the real world information to be represented is of imperfect nature and the classical crisp true, false approximation is not adequate. A general framework, called Parametric Deductive Databases with Uncerta ..."
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Cited by 16 (10 self)
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The management of uncertain information in logic programs becomes to be important whenever the real world information to be represented is of imperfect nature and the classical crisp true, false approximation is not adequate. A general framework, called Parametric Deductive Databases with Uncertainty (PDDU) framework [10], was proposed as a unifying umbrella for many existing approaches towards the manipulation of uncertainty in logic programs. We extend PDDU with (nonmonotonic) negation, a wellknown and important feature of logic programs.
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.
Anyworld assumptions in logic programming
, 2005
"... Due to the usual incompleteness of information representation, any approach to assign a semantics to logic programs has to rely on a default assumption on the missing information. The stable model semantics, that has become the dominating approach to give semantics to logic programs, relies on the C ..."
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Cited by 12 (3 self)
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Due to the usual incompleteness of information representation, any approach to assign a semantics to logic programs has to rely on a default assumption on the missing information. The stable model semantics, that has become the dominating approach to give semantics to logic programs, relies on the Closed World Assumption (CWA), which asserts that by default the truth of an atom is false. There is a second wellknown assumption, called Open World Assumption (OWA), which asserts that the truth of the atoms is supposed to be unknown by default. However, the CWA, the OWA and the combination of them are extremal, though important, assumptions over a large variety of possible assumptions on the truth of the atoms, whenever the truth is taken from an arbitrary truth space. The topic of this paper is to allow any assignment (i.e. interpretation), over a truth space, to be a default assumption. Our main result is that our extension is conservative in the sense that under the “everywhere false ” default assumption (CWA) the usual stable model semantics is captured. Due to the generality and the purely algebraic nature of our approach, it abstracts from the particular formalism of choice and the results may be applied in other contexts as well.
Query answering under the anyworld assumption for normal logic programs
 In Proceedings of the 10th International Conference on Knowledge Representation (KR06
, 2006
"... Recently, in (Loyer & Straccia 2005) the AnyWorld Assumption (AWA) has been introduced for normal logic programs as a generalization of the wellknown notions of Closed World Assumption (CWA) and the Open World Assumption (OWA). The AWA allows any assignment (i.e. interpretation), over a truth ..."
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Cited by 10 (4 self)
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Recently, in (Loyer & Straccia 2005) the AnyWorld Assumption (AWA) has been introduced for normal logic programs as a generalization of the wellknown notions of Closed World Assumption (CWA) and the Open World Assumption (OWA). The AWA allows any assignment (i.e. interpretation), over a truth space (bilattice), to be a default assumption and, thus, the CWA and OWA are just special cases. While a declarative and a fixedpoint characterization for normal logic programs under the AWA has been given in (Loyer & Straccia 2005), the topic of this paper is to provide a simple, yet general topdown query answering procedure for this setting.
Hybrid probabilistic logic programming with nonmonotoic negation
 In Twenty First International Conference on Logic Programming
, 2005
"... Abstract. 1 In [20], a new Hybrid Probabilistic Logic Programs framework is proposed, and a new semantics is developed to enable encoding and reasoning about realworld applications. In this paper, we extend the language of Hybrid Probabilistic Logic Programs framework in [20] to allow nonmonotonic ..."
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Cited by 4 (3 self)
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Abstract. 1 In [20], a new Hybrid Probabilistic Logic Programs framework is proposed, and a new semantics is developed to enable encoding and reasoning about realworld applications. In this paper, we extend the language of Hybrid Probabilistic Logic Programs framework in [20] to allow nonmonotonic negation, and define two alternative semantics: stable probabilistic model semantics and probabilistic wellfounded semantics. Stable probabilistic model semantics and probabilistic wellfounded semantics generalize stable model semantics and wellfounded semantics of traditional normal logic programs, and they reduce to the semantics of original Hybrid Probabilistic Logic programs framework of [20]. It is the first time that two different semantics for Hybrid Probabilistic Programs with nonmonotonic negation as well as their relationship are described. This development provides a foundational ground for developing computational methods for computing the proposed semantics. Furthermore, it makes it clearer how to characterize nonmonotonic negation in probabilistic logic programming frameworks for commonsense reasoning. 1
Nonmonotonic Negation in Hybrid Probabilistic Logic Programs
"... In [23], a new Hybrid Probabilistic Logic Programs framework has been proposed, and a new semantics has been developed to enable encoding and reasoning about realworld applications. In this paper, the language of Hybrid Probabilistic Logic Programs framework of [23] is extended to allow nonmonoton ..."
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In [23], a new Hybrid Probabilistic Logic Programs framework has been proposed, and a new semantics has been developed to enable encoding and reasoning about realworld applications. In this paper, the language of Hybrid Probabilistic Logic Programs framework of [23] is extended to allow nonmonotonic negation, and two alternative semantics are defined: stable probabilistic model semantics and probabilistic wellfounded semantics. Stable probabilistic model semantics and probabilistic wellfounded semantics generalize stable model semantics and wellfounded semantics of traditional normal logic programs, and they reduce to the semantics of original Hybrid Probabilistic Logic programs framework of [23] for programs without negation. It is the first time that two di#erent semantics for Hybrid Probabilistic Programs with nonmonotonic negation as well as their relationships are described. This development provides a foundational ground for developing computational methods for computing the proposed semantics. Furthermore, it makes it clearer how to characterize nonmonotonic negation in probabilistic logic programming frameworks for commonsense reasoning.
in normal residuated logic programs
, 2010
"... On the existence of stable models ..."
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Under consideration for publication in Theory and Practice of Logic Programming 1 Reducing Fuzzy Answer Set Programming to Model Finding in Fuzzy Logics
"... In recent years answer set programming has been extended to deal with multivalued predicates. The resulting formalisms allows for the modeling of continuous problems as elegantly as ASP allows for the modeling of discrete problems, by combining the stable model semantics underlying ASP with fuzzy l ..."
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In recent years answer set programming has been extended to deal with multivalued predicates. The resulting formalisms allows for the modeling of continuous problems as elegantly as ASP allows for the modeling of discrete problems, by combining the stable model semantics underlying ASP with fuzzy logics. However, contrary to the case of classical ASP where many efficient solvers have been constructed, to date there is no efficient fuzzy answer set programming solver. A wellknown technique for classical ASP consists of translating an ASP program P to a propositional theory whose models exactly correspond to the answer sets of P. In this paper, we show how this idea can be extended to fuzzy ASP, paving the way to implement efficient fuzzy ASP solvers that can take advantage of existing fuzzy logic reasoners. To appear in Theory and Practice of Logic Programming (TPLP).