Labeled RDF

Abstract

There are different proposals to extend RDF model theory allowing a treatment of uncertainty within the language. This works proposes a unified approach for RDF graph and statement labeling. This approach is more general than fuzzy and temporal labels and can be used to label RDF graphs with membership degrees, timestamps, or with a combination of labelings. Starting from a definition of labeled sets and labeled logic, we define labeled RDF and labeled RDF Schema. A partial ordering among labels allows qualitative treatment of uncertainty. I. UNCERTAINTY IN LOGICAL LANGUAGESRDF model theory [1], like classical logic, is based on the strongest simplification about truth: a sentence can be either true of false. This simplification of reality is indeed the strongest conceivable simplification. It is possible to better approximate shades of truth allowing more than two values.Three valued logic [2] allows a truth value to be undefined or undetermined, and imposes a rule of regularity: if some undefined propositional letter p is given a value of either true or false, then the value of any formula using p should never change from true to false or from false to true [3].Four valued logic [4] distinguishes uncertainty due to undefined truth values to uncertainty due to inconsistent truth values. The four truth values, denoted as t (true), f (false), ⊥ (undetermined), and (inconsistent) are partially ordered according to truth (t is "more true" than f , whereas and ⊥ have intermediate values), and according to amount of knowledge (⊥ has the minimum amount, the maximum, and t and f have intermediate values). Four-valued logic allows paraconsistent reasoning, i.e. reasoning in presence of inconsistencies; an application is the mapping of a description logic-based OWL ontology to an ontology in a fourvalued description logic, allowing to reason with inconsistent ontologies [5]. Four-valued logic can further be generalized to bilattice-based logic [6], where the set of truth value is a lattice with two partial orders.Annotated logic programs [7] contain labeled clauses; labels forms a lattice. Annotated logic programs generalize to a lattice of labels the concept of quantitative deduction [8], where each clause receive a numerical attenuation value.Fuzzy logic is a logic where a proposition can be true or false to some degree. Extending RDF with a fuzzy logic semantics [9][10] allows to attach a degree to each assertion. Truth degrees are given by numbers, so each degree is comparable with any other degree, i.e. they have a total ordering. ).In a previous work [9] we introduced a fuzzy semantics for RDF and RDF Schema. The fuzzy semantics allows to deal with the kind of uncertainty due to vagueness. Although one of the motivating use case of fuzzy RDF was the encoding of trust metadata [11], the use of fuzzy membership values to express trustworthiness is not appropriate. When the extralogic value attached to a tripe is related to provenance, a numerical value is difficult to interpret. While it is true that we can genericall...