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15
Monotonic and Residuated Logic Programs
, 2001
"... In this paper we define the rather general framework of Monotonic Logic Programs, where the main results of (definite) logic programming are validly extrapolated. Whenever defining new logic programming extensions, we can thus turn our attention to the stipulation and study of its intuitive algebrai ..."
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Cited by 45 (10 self)
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In this paper we define the rather general framework of Monotonic Logic Programs, where the main results of (definite) logic programming are validly extrapolated. Whenever defining new logic programming extensions, we can thus turn our attention to the stipulation and study of its intuitive algebraic properties within the very general setting. Then, the existence of a minimum model and of a monotonic immediate consequences operator is guaranteed, and they are related as in classical logic programming. Afterwards we study the more restricted class of residuated logic programs which is able to capture several quite distinct logic programming semantics. Namely: Generalized Annotated Logic Programs, Fuzzy Logic Programming, Hybrid Probabilistic Logic Programs, and Possibilistic Logic Programming. We provide the embedding of possibilistic logic programming.
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 41 (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.
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 22 (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.
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 17 (6 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).
Termination Results for Sorted MultiAdjoint Logic Programs
 In Information Processing and Management of Uncertainty for KnowledgeBased Systems, IPMU’04. Accepted
"... In this paper we present a logic programmingbased language allowing for the combination of several adjoint lattices of truthvalues. A model and xpoint theory are presented, but the main contribution of the paper is the study of general properties guaranteeing termination of all queries. New ..."
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Cited by 10 (4 self)
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In this paper we present a logic programmingbased language allowing for the combination of several adjoint lattices of truthvalues. A model and xpoint theory are presented, but the main contribution of the paper is the study of general properties guaranteeing termination of all queries. New results are presented and related to other alternative formalisms.
A MultiAdjoint Logic Approach to Abductive Reasoning
 In Logic Programming, ICLP’01
, 2001
"... Multiadjoint logic programs has been recently introduced [9, 10] as a generalization of monotonic logic programs [2, 3], 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 4 (4 self)
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Multiadjoint logic programs has been recently introduced [9, 10] as a generalization of monotonic logic programs [2, 3], in that simultaneous use of several implications in the rules and rather general connectives in the bodies are allowed.
MultiAdjoint Logic Programming
 In Proc. of the 10th Int. Conf. on Information Processing and Managment of Uncertainty in KnowledgeBased Systems, (IPMU04
, 2004
"... A synthesis of results of the recently introduced paradigm of multiadjoint logic programming is presented. These results range from a proof theory together with some (quasi)completeness results to general termination results, and from the neurallike implementation of its fixpoint semantics ..."
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Cited by 2 (0 self)
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A synthesis of results of the recently introduced paradigm of multiadjoint logic programming is presented. These results range from a proof theory together with some (quasi)completeness results to general termination results, and from the neurallike implementation of its fixpoint semantics to the more general biresiduated multiadjoint logic programming and its relationship with other approaches.
Fuzzy Logic Programming and Fuzzy Control by
"... Abstract. The paper concerns fuzzy logic programming. As an example, we show that is not restrictive to confine ourselves to fuzzy Herbrand interpretations in giving a semantics for fuzzy programs. Also, we show that the resulting apparatus gives a unifying theoretical framework for fuzzy control. ..."
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Cited by 2 (0 self)
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Abstract. The paper concerns fuzzy logic programming. As an example, we show that is not restrictive to confine ourselves to fuzzy Herbrand interpretations in giving a semantics for fuzzy programs. Also, we show that the resulting apparatus gives a unifying theoretical framework for fuzzy control.
Łukasiewicz logic: From proof systems to logic programming
 Logic Journal of the IGPL
, 2005
"... We present logic programming style “goaldirected ” proof methods for ̷Lukasiewicz logic ̷L that both have a logical interpretation, and provide a suitable basis for implementation. We introduce a basic version, similar to goaldirected calculi for other logics, and make refinements to improve effic ..."
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Cited by 1 (1 self)
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We present logic programming style “goaldirected ” proof methods for ̷Lukasiewicz logic ̷L that both have a logical interpretation, and provide a suitable basis for implementation. We introduce a basic version, similar to goaldirected calculi for other logics, and make refinements to improve efficiency and obtain termination. We then provide an algorithm for fuzzy logic programming in Rational Pavelka logic RPL, an extension of ̷L with rational constants. Keywords: ̷Lukasiewicz Logics, Fuzzy Logics, GoalDirected Methods, Logic Programming 1