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A generalization of the homogenization process needed for the neural implementation of multi-adjoint 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...
Motivation for this paper are classification problems in which data can not be clearly divided into positive and negative examples, especially data in which there is a monotone hierarchy (degree, preference) of more or less positive (negative) examples. We present a new formulation of a fuzzy inductive logic programming task in the framework of fuzzy logic in narrow sense. Our construction is based on a syntactical equivalence of fuzzy logic programs FLP and a restricted class of generalised annotated...
The logic of signed formula can be used to reason about a wide variety of multiple-valued logics [Häh94b, LMR97]. The formal theoretical foundation of multiple-valued logic programming based on signed formulas is set forth in [Lu96]. The current paper is an investigation into the operational semantics of such signed logic programming. The connection of signed logic programming to constraint logic programming is presented, search space issues are briefly discussed for both general and special cases,...
In this paper we argue that for fuzzy unification we need a procedural and declarative semantics (as opposed to the two valued case, where declarative semantics is hidden in the requirement that unified terms are syntactically – letter by letter – identical). We present an extension of the syntactic model of unification to allow near matches, defined using a similarity relation. We work in Hájek’s fuzzy logic in narrow sense. We base our semantics on a formal model of fuzzy logic programming extended...
Inf-Datalog extends the usual least fixpoint semantics of Datalog with greatest fixpoint semantics: we defined inf-Datalog and characterized the expressive power of various fragments of inf-Datalog in [16]. In the present paper, we study the complexity of query evaluation on finite models for (various fragments of) inf-Datalog. We deduce a unified and elementary proof that global model-checking (i.e. computing all nodes satisfying a formula in a given structure) has 1. quadratic data complexity...
Inf-Datalog
extends the usual least fixpoint semantics of Datalog with greatest
fixpoint semantics: we defined inf-Datalog and characterized the
expressive power of various fragments of inf-Datalog in [CITE].
In the present paper, we study the
complexity of query evaluation on finite models
for (various fragments of) inf-Datalog.
We deduce a unified and elementary proof that global model-checking
(i.e. computing all nodes satisfying a formula in a given structure) has
1. quadratic data complexity...
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