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MultiAdjoint Logic Programming with Continuous Semantics
 Lect. Notes in Artificial Intelligence 2173
, 2001
"... Considering different implication operators, such as Lukasiewicz, Gödel or product implication in the same logic program, naturally leads to the allowance of several adjoint pairs in the lattice of truthvalues. In this paper we apply this idea to introduce multiadjoint logic programs as an extensi ..."
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Cited by 39 (18 self)
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Considering different implication operators, such as Lukasiewicz, Gödel or product implication in the same logic program, naturally leads to the allowance of several adjoint pairs in the lattice of truthvalues. In this paper we apply this idea to introduce multiadjoint logic programs as an extension of monotonic logic programs. The continuity of the immediate consequences operators is proved and the assumptions required to get continuity are further analysed.
Antitonic Logic Programs
, 2001
"... In a previous work we have de ned Monotonic Logic Programs which extend definite logic programming to arbitrary complete lattices of truthvalues with an appropriate notion of implication. We have shown elsewhere that this framework is general enough to capture Generalized Annotated Logic Programs, ..."
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Cited by 30 (10 self)
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In a previous work we have de ned Monotonic Logic Programs which extend definite logic programming to arbitrary complete lattices of truthvalues with an appropriate notion of implication. We have shown elsewhere that this framework is general enough to capture Generalized Annotated Logic Programs, Probabilistic Deductive Databases, Possibilistic Logic Programming, Hybrid Probabilistic Logic Programs and Fuzzy Logic Programming [3, 4]. However, none of these semantics define a form of nonmonotonic negation, which is fundamental for several knowledge representation applications. In the spirit of our previous work, we generalise our framework of Monotonic Logic Programs to allow for rules with arbitrary antitonic bodies over general complete lattices, of which normal programs are a special case. We then show that all the standard logic programming theoretical results carry over to Antitonic Logic Programs, defining Stable Model and Wellfounded Model alike semantics.
A Procedural Semantics for MultiAdjoint Logic Programming
 In Progress in Artificial Intelligence, EPIA’01
, 2001
"... Multiadjoint logic program generalise monotonic logic programs introduced in [1] in that simultaneous use of several implications in the rules and rather general connectives in the bodies are allowed. ..."
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Cited by 22 (13 self)
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Multiadjoint logic program generalise monotonic logic programs introduced in [1] in that simultaneous use of several implications in the rules and rather general connectives in the bodies are allowed.
Similaritybased unification: a multiadjoint approach. Fuzzy sets and systems
 In Proc. EUSFLAT Conference in Fuzzy Logic and Technology
, 2002
"... The aim of this paper is to build a formal model for fuzzy unification in multiadjoint logic programs containing both a declarative and a procedural part, and prove its soundness and completeness. Our approach is based on a general framework for logic programming, which gives a formal model of fuzz ..."
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Cited by 20 (5 self)
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The aim of this paper is to build a formal model for fuzzy unification in multiadjoint logic programs containing both a declarative and a procedural part, and prove its soundness and completeness. Our approach is based on a general framework for logic programming, which gives a formal model of fuzzy logic programming extended by fuzzy similarities and axioms of firstorder logic with equality.
Hybrid Probabilistic Logic Programs as Residuated Logic Programs
, 2002
"... In this paper we show the embedding of Hybrid Probabilistic Logic Programs into the rather general framework of Residuated Logic Programs, where the main results of (definite) logic programming are validly extrapolated, namely the extension of the immediate consequences operator of van Emden and Kow ..."
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Cited by 19 (4 self)
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In this paper we show the embedding of Hybrid Probabilistic Logic Programs into the rather general framework of Residuated Logic Programs, where the main results of (definite) logic programming are validly extrapolated, namely the extension of the immediate consequences operator of van Emden and Kowalski. The importance of this result is that for the first time a framework encompassing several quite distinct logic programming semantics is described, namely Generalized Annotated Logic Programs, Fuzzy Logic Programming, Hybrid Probabilistic Logic Programs, and Possibilistic Logic Programming. Moreover, the embedding provides a more general semantical structure paving the way for defining paraconsistent probabilistic reasoning with a logic programming semantics.
Sorted Monotonic Logic Programs and their Embeddings
, 2004
"... In this paper we present a logic programmingbased language allowing for the combination of several lattices of truthvalues under arbitrary monotonic operators. A model and fixpoint theory are presented, but the main contributions of the paper are the embedding results of a series of existing l ..."
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Cited by 18 (3 self)
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In this paper we present a logic programmingbased language allowing for the combination of several lattices of truthvalues under arbitrary monotonic operators. A model and fixpoint theory are presented, but the main contributions of the paper are the embedding results of a series of existing logic programming semantics dealing with uncertainty, vagueness, or probabilistic reasoning. A major benefit of this work is to provide a comparative overview of the several proposals, all of which are translate into a single unified general framework. This paves the way for the construction of integrated logic programmingbased systems capturing several facets of human/formal uncertainty reasoning. We overview, and compare more than twenty different proposals in the extant literature.
Sorted MultiAdjoint Logic Programs: Termination Results and Applications
"... A general framework of logic programming allowing for the combination of several adjoint lattices of truthvalues is presented. The main contribution is a new sufficient condition which guarantees termination of all queries for the fixpoint semantics for an interesting class of programs. Several ..."
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Cited by 16 (5 self)
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A general framework of logic programming allowing for the combination of several adjoint lattices of truthvalues is presented. The main contribution is a new sufficient condition which guarantees termination of all queries for the fixpoint semantics for an interesting class of programs. Several extensions of these conditions are presented and related to some wellknown formalisms for probabilistic logic programming.
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 16 (5 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).
Uncertainty Treatment in the Rule Interchange Format: From Encoding to Extension
"... Harold.Boley AT nrc.gc.ca Abstract. The Rule Interchange Format (RIF) is an emerging W3C format that allows rules to be exchanged between rule systems. Uncertainty is an intrinsic feature of real world knowledge, hence it is important to take it into account when building logic rule formalisms. Howe ..."
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Cited by 13 (0 self)
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Harold.Boley AT nrc.gc.ca Abstract. The Rule Interchange Format (RIF) is an emerging W3C format that allows rules to be exchanged between rule systems. Uncertainty is an intrinsic feature of real world knowledge, hence it is important to take it into account when building logic rule formalisms. However, the set of truth values in the Basic Logic Dialect (RIFBLD) currently consists of only two values (t and f). In this paper, we first present two techniques of encoding uncertain knowledge and its fuzzy semantics in RIFBLD presentation syntax. We then propose an extension leading to an Uncertainty Rule Dialect (RIFURD) to support a direct representation of uncertain knowledge. In addition, rules in Logic Programs (LP) are often used in combination with the other widelyused knowledge representation formalism of the Semantic Web, namely Description Logics (DL), in order to provide greater expressive power. To prepare DL as well as LP extensions, we present a fuzzy extension to Description Logic Programs (DLP), called Fuzzy DLP, and discuss its mapping to RIF. Such a formalism not only combines DL with LP, as in DLP, but also supports uncertain Description Logics (DL) and Logic Programs (LP) are the two main categories of knowledge
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 operators fo ..."
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Cited by 8 (4 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.