Logic reasoning under data veracity concerns

Abstract

Logic reasoning involving big data often requires the proper handling of data veracity. Indeed with data that cannot be trusted to the same extent, users should at least be aware on the trust they can have in the obtained reasoning. In this paper, we propose a novel logic framework that is based on so-called L-grades. L-grades are a special case of Zadeh's Z-numbers, consisting of a pair (s,c)∈[0,1]2 in which s is a suitability grade (or satisfaction grade) and c is a confidence grade denoting how confident we can be on s. Both grades are further processed using fuzzy logic. A novel negation operator and novel conjunction and disjunction operators satisfying commutativity, associativity, but not distributivity properties are proposed. Furthermore, so-called sibling aggregators for L-grades are introduced and studied. With this framework we aim to contribute to explainable computational intelligence. The practical applicability of L-grades is discussed based on the demand for more informative, explainable results in the TILES decision support system for sand extraction from the North Sea seabed.