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20
A uniform approach to logic programming semantics
 Theory and Practice of Logic Programming
, 2005
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An Encompassing Framework for Paraconsistent Logic Programs
 J. Applied Logic
, 2003
"... We propose a framework which extends Antitonic Logic Programs [13] to an arbitrary complete bilattice of truthvalues, where belief and doubt are explicitly represented. Inspired by Ginsberg and Fitting 's bilattice approaches, this framework allows a precise de nition of important operato ..."
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Cited by 17 (6 self)
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We propose a framework which extends Antitonic Logic Programs [13] to an arbitrary complete bilattice of truthvalues, where belief and doubt are explicitly represented. Inspired by Ginsberg and Fitting 's bilattice approaches, this framework allows a precise de nition of important operators found in logic programming, such as explicit and default negation. In particular, it leads to a natural semantical integration of explicit and default negation through the Coherence Principle [38], according to which explicit negation entails default negation. We then de ne Coherent Answer Sets, and the Paraconsistent Wellfounded Model semantics, generalising many paraconsistent semantics for logic programs. In particular, Paraconsistent WellFounded Semantics with eXplicit negation (WFSXp ) [3, 11]. The framework is an extension of Antitonic Logic Programs for most cases, and is general enough to capture Probabilistic Deductive Databases, Possibilistic Logic Programming, Hybrid Probabilistic Logic Programs, and Fuzzy Logic Programming. Thus, we have a powerful mathematical formalism for dealing simultaneously with default, paraconsistency, and uncertainty reasoning. Results are provided about how our semantical framework deals with inconsistent information and with its propagation by the rules of the program.
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.
U.: Epistemic foundation of the wellfounded semantics over bilattices
 MFCS 2004. LNCS
, 2004
"... Abstract. We define new, both modeltheoretical and fixpointbased, characterizations of the wellfounded semantics for logic programs in the general setting of bilattices. This work lights the role of the CWA, used in the wellfounded semantics as a carrier of falsehood, and shows that the definiti ..."
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Cited by 7 (3 self)
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Abstract. We define new, both modeltheoretical and fixpointbased, characterizations of the wellfounded semantics for logic programs in the general setting of bilattices. This work lights the role of the CWA, used in the wellfounded semantics as a carrier of falsehood, and shows that the definition of that semantics does not require any separation of positive and negative information nor any program transformation.
Uncertainty modeling by bilatticebased squares and triangles
 IEEE Transactions on Fuzzy Systems
"... Abstract—In this paper, Ginsberg’s/Fitting’s theory of bilattices, and in particular the associated constructs of bilatticebased squares and triangles, is introduced as an attractive framework for the representation of uncertain and potentially conflicting information, paralleling Goguen’sfuzzy se ..."
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Cited by 5 (4 self)
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Abstract—In this paper, Ginsberg’s/Fitting’s theory of bilattices, and in particular the associated constructs of bilatticebased squares and triangles, is introduced as an attractive framework for the representation of uncertain and potentially conflicting information, paralleling Goguen’sfuzzy set theory. We recall some of the advantages of bilatticebased frameworks for handling fuzzy sets and systems, provide the related structures with adequately defined graded versions of the basic logical connectives, and study their properties and relationships. Index Terms—Bilattices, bilatticebased squares and triangles, implicators, MValgebras, negators, tnorms and tconorms. I.
Reasoning with different levels of uncertainty
 Journal of Applied NonClassical Logics
, 2003
"... ABSTRACT. We introduce a family of preferential logics that are useful for handling information with different levels of uncertainty. The corresponding consequence relations are nonmonotonic, paraconsistent, adaptive, and rational. It is also shown that the formalisms in this family can be embedded ..."
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Cited by 4 (3 self)
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ABSTRACT. We introduce a family of preferential logics that are useful for handling information with different levels of uncertainty. The corresponding consequence relations are nonmonotonic, paraconsistent, adaptive, and rational. It is also shown that the formalisms in this family can be embedded in corresponding fourvalued logics with at most three uncertainty levels, and that reasoning with these logics can be simulated by algorithms for processing circumscriptive theories, such as DLS and SCAN.
A topdown query answering procedure for normal logic programs under the anyworld assumption
 In Proc. ECSQARU07, number 4724 in LNCS
, 2007
"... Abstract. 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 de ..."
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Cited by 4 (0 self)
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Abstract. 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. To answer queries, we provide a novel and simple topdown procedure.
A Paraconsistent Logic Programming Approach for Querying Inconsistent Knowledge Bases
"... When integrating data coming from multiple different sources we are faced with the possibility of inconsistency in databases. A paraconsistent approach for knowledge base integration allows keeping inconsistent information and reasoning in its presence. In this paper, we use a paraconsistent logic ( ..."
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When integrating data coming from multiple different sources we are faced with the possibility of inconsistency in databases. A paraconsistent approach for knowledge base integration allows keeping inconsistent information and reasoning in its presence. In this paper, we use a paraconsistent logic (LFI1) as the underlying logic for the specification of PDatalog, a deductive query language for databases containing inconsistent information. We present a declarative semantics which captures the desired meaning of a recursive query executed over a database containing inconsistent facts and whose rules allow infering information from inconsistent premises. We also present a bottomup evaluation method for PDatalog programs based on an alternating fixpoint operator.