Paraconsistent Logic Programs with Four-Valued Rough Sets

Abstract

Abstract. This paper presents a language for defining four-valued rough sets and to reason about them. Our framework brings together two major fields: rough sets and paraconsistent logic programming. On the one hand it provides a paraconsistent approach, based on four-valued rough sets, for integrating knowledge from different sources and reasoning in the presence of inconsistencies. On the other hand, it also caters for a specific type of uncertainty that originates from the fact that an agent may perceive different objects of the universe as being indiscernible. This paper extends the ideas presented in [9]. Our language allows the user to define similarity relations and use the approximations induced by them in the definition of other four-valued sets. A positive aspect is that it allows users to tune the level of uncertainty or the source of uncertainty that best suits applications.

Modeling and Reasoning with Paraconsistent Rough Sets

“…Our aim is to present a rule language for defining paraconsistent sets (see [22]). We start by defining formally the rule language and presenting some examples illustrating the idea.…”

“…Namely, an object o belongs to the lower approximation of a given set A whenever all objects indiscernible from o belong to A and o belongs to its upper approximation, when there are objects indiscernible from o belonging to A. Indiscernibility is modeled by similarity relations reflecting limited perceptual capabilities as well as incomplete and imprecise knowledge. Such approximations naturally lead to three-and four-valued logics (see, e.g., [6,10,14,21,32,22]). …”

“…The language discussed in this paper is based on ideas of our previous work [21,32,22] developing a four-valued framework for rough sets. In this approach membership function, set containment and set operations are four-valued, where logical values are t (true), f (false), i (inconsistent) and u (unknown).…”

Fusing Approximate Knowledge from Distributed Sources

“…For example, one might not want the relation be transitive since similar objects do not naturally chain in a transitive manner (see, e.g., [1,6,3,10]). …”

Paraconsistent and Approximate Semantics for the OWL 2 Web Ontology Language

“…Truth values in this logic represent truth (t), falsity (f), the lack of knowledge (u) and inconsistency (i). However, there are serious problems with using Belnap's logic for Semantic Web (see [11,25,15]). In [15] together with Sza las we gave a three-valued paraconsistent semantics for the DL SHIQ, which is related to the DL SHOIN used for OWL 1.1.…”