Modeling and Reasoning with Paraconsistent Rough Sets

Abstract

We present a language for defining paraconsistent rough sets and reasoning about them. Our framework relates and brings together two major fields: rough sets [23] and paraconsistent logic programming [9]. To model inconsistent and incomplete information we use a four-valued logic.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).We investigate properties of paraconsistent rough sets as well as develop a paraconsistent rule language, providing basic computational machinery for our approach.

Logic Fragments: A Coordination Model Based on Logic Inference

“…Several kinds of logics present interesting features to model and validate coordination primitives: (i) paraconsistent logics (e.g. [17]) and (ii) spatial-temporal logics, to assert properties depending on location and time parameters of system components. We plan also to realise an implementation of the model, including several semantics for Logic Fragments taking inspiration from the coordination primitives presented in [7].…”

“…The advent of new families of logic languages (e.g. [17]) has enriched the paradigm of logic programming, allowing, among other things, practical formalisation and manipulation of data inconsistency, knowledge representation of partial information and constraints satisfaction. By combining those logics with a chemical-based coordination model, we argue that global properties can be verified at design time.…”

A paraconsistent approach to actions in informationally complex environments

“…The four-valued logic R 4 has originally been introduced in [37] (see also [34,36,50,55]). Below we present its main features and motivations behind its design choices.…”

Logical foundations and complexity of 4QL, a query language with unrestricted negation

“…This paper presents a solution to this problem. A preliminary idea of a four-valued rule language not admitting disjunction in rule bodies appeared in our previous work [VMS09].…”

“…These methodological assumptions led to a DATALOG ¬¬ -like query language, 4QL, founded on a four-valued semantics. The semantics employs the logic introduced in [MSV08, VMS09] with truth values: 'true', 'false', 'inconsistent' and 'unknown', further denoted by t, f, i and u, respectively.…”