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51
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 50 (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.
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 32 (7 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.
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 26 (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.
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 21 (7 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.
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 20 (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.
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 18 (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).
Annotated answer set programming
 In: Proceedings of the 11th International Conference on Information Processing and Management of Uncertainty in KnowledgeBased Systems (IPMU06
, 2006
"... We present Annotated Answer Set Programming, that extends the expressive power of disjunctive logic programming with annotation terms, taken from the generalized annotated logic programming framework. ..."
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Cited by 10 (0 self)
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We present Annotated Answer Set Programming, that extends the expressive power of disjunctive logic programming with annotation terms, taken from the generalized annotated logic programming framework.
A Completeness Theorem for MultiAdjoint Logic Programming
 In Proc. FUZZIEEE’01. The 10th IEEE International Conference on Fuzzy Systems, IEEE
, 2001
"... Mukiadjoint logic programs generalise monotonic and residuated logic pro grams [21 in that simultaneous use of several implications in the rules and rather general connectives in the bodies are allowed. As our approach has continuous fixpoint semantics, in this work, a procedural semantics is g ..."
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Cited by 6 (2 self)
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Mukiadjoint logic programs generalise monotonic and residuated logic pro grams [21 in that simultaneous use of several implications in the rules and rather general connectives in the bodies are allowed. As our approach has continuous fixpoint semantics, in this work, a procedural semantics is given for the paradigm of multiadjoint logic programming and a completeness result is proved.
Towards Biresiduated MultiAdjoint Logic Programming
 IN PROC. CAEPIA’03, LECT. NOTES IN ARTIFICIAL INTELLIGENCE 3040:608–617
, 2003
"... Multiadjoint logic programs were recently proposed as a generalization of monotonic and residuated logic programs, in that simultaneous use of several implications in the rules and rather general connectives in the bodies are allowed. In this work, the need of biresiduated pairs is justified thr ..."
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Cited by 6 (4 self)
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Multiadjoint logic programs were recently proposed as a generalization of monotonic and residuated logic programs, in that simultaneous use of several implications in the rules and rather general connectives in the bodies are allowed. In this work, the need of biresiduated pairs is justified through the study of a very intuitive family of operators, which turn out to be not necessarily commutative and associative and, thus, might have two different residuated implications; finally, we introduce the framework of biresiduated multiadjoint logic programming and sketch some considerations on its fixpoint semantics.
A neural implementation of multiadjoint logic programming
 Journal of Applied Logic
, 2004
"... A generalization of the homogenization process needed for the neural implementation of multiadjoint logic programming (a unifying theory to deal with uncertainty, imprecise data or incomplete information) is presented here. The idea is to allow to represent a more general family of adjoint pairs, b ..."
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Cited by 5 (2 self)
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A generalization of the homogenization process needed for the neural implementation of multiadjoint logic programming (a unifying theory to deal with uncertainty, imprecise data or incomplete information) is presented here. The idea is to allow to represent a more general family of adjoint pairs, but maintaining the advantage of the existing implementation recently introduced in [6]. The soundness of the transformation is proved and its complexity is analysed. In addition, the corresponding generalization of the neurallike implementation of the fixed point semantics of multiadjoint is presented. 1