Results 1  10
of
25
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 ..."
Abstract

Cited by 44 (9 self)
 Add to MetaCart
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.
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 ..."
Abstract

Cited by 19 (4 self)
 Add to MetaCart
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 ..."
Abstract

Cited by 18 (3 self)
 Add to MetaCart
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.
Fuzzy Description Logic Programs under the Answer Set Semantics for the Semantic Web
 WEB, SECOND INTERNATIONAL CONFERENCE, RULEML
, 2006
"... Vagueness and imprecision abound in multimedia information processing and retrieval. In this paper, towards dealing with vagueness and imprecision in the reasoning layers of the Semantic Web, we present an approach to fuzzy description logic programs under the answer set semantics. We generalize nor ..."
Abstract

Cited by 17 (7 self)
 Add to MetaCart
Vagueness and imprecision abound in multimedia information processing and retrieval. In this paper, towards dealing with vagueness and imprecision in the reasoning layers of the Semantic Web, we present an approach to fuzzy description logic programs under the answer set semantics. We generalize normal description logic programs (dlprograms) under the answer set semantics by fuzzy vagueness and imprecision. We define a canonical semantics of positive and stratified fuzzy dlprograms in terms of a unique least model and iterative least models, respectively. We then define the answer set semantics of general fuzzy dlprograms, and show in particular that all answer sets of a fuzzy dlprogram are minimal models, and that the answer set semantics of positive and stratified fuzzy dlprograms coincides with their canonical least model and iterative least model semantics, respectively. Furthermore, we also provide a characterization of the canonical semantics of positive and stratified fuzzy dlprograms in terms of a fixpoint and an iterative fixpoint semantics, respectively.
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). ..."
Abstract

Cited by 16 (5 self)
 Add to MetaCart
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).
Query Answering in Normal Logic Programs under Uncertainty
 8TH EUROPEAN CONFERENCES ON SYMBOLIC AND QUANTITATIVE APPROACHES TO REASONING WITH UNCERTAINTY (ECSQARU05), NUMBER 3571
, 2005
"... We present a simple, yet general topdown query answering procedure for normal logic programs over lattices and bilattices, where functions may appear in the rule bodies. Its interest relies on the fact that many approaches to paraconsistency and uncertainty in logic programs with or without nonmo ..."
Abstract

Cited by 10 (5 self)
 Add to MetaCart
We present a simple, yet general topdown query answering procedure for normal logic programs over lattices and bilattices, where functions may appear in the rule bodies. Its interest relies on the fact that many approaches to paraconsistency and uncertainty in logic programs with or without nonmonotonic negation are based on bilattices or lattices, respectively.
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 ..."
Abstract

Cited by 8 (4 self)
 Add to MetaCart
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.
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 ..."
Abstract

Cited by 8 (1 self)
 Add to MetaCart
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.
Possibilistic stable models
 Nonmonotonic Reasoning, Answer Set Programming and Constraints, volume 05171 of Dagstuhl Seminar Proceedings. Internationales Begegnungs und Forschungszentrum für Informatik (IBFI), Schloss Dagstuhl
, 2005
"... In this work, we define a new framework in order to improve the knowledge representation power of Answer Set Programming paradigm. Our proposal is to use notions from possibility theory to extend the stable model semantics by taking into account a certainty level, expressed in terms of necessity mea ..."
Abstract

Cited by 8 (1 self)
 Add to MetaCart
In this work, we define a new framework in order to improve the knowledge representation power of Answer Set Programming paradigm. Our proposal is to use notions from possibility theory to extend the stable model semantics by taking into account a certainty level, expressed in terms of necessity measure, on each rule of a normal logic program. First of all, we introduce possibilistic definite logic programs and show how to compute the conclusions of such programs both in syntactic and semantic ways. The syntactic handling is done by help of a fixpoint operator, the semantic part relies on a possibility distribution on all sets of atoms and we show that the two approaches are equivalent. In a second part, we define what is a possibilistic stable model for a normal logic program, with default negation. Again, we define a possibility distribution allowing to determine the stable models. 1
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. ..."
Abstract

Cited by 7 (0 self)
 Add to MetaCart
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.