On levels of inconsistency of sets of premises

Abstract

A certain approach to paraconsistency was initiated by works of R. Jennings and P. Schotch. In their „Inference and necessity’” (1980) they proposed a notion of a level of inconsistency (incoherence) of a given set of premises. This level is a measure that assigns to a given set of premises X, the least number of elements of covers of X, that consist of consistent subsets of X. The idea of the level of inconsistency allows to formulate a paraconsistent inference relation called by the authors forcing. The proposed approach is known as preservationism. Simi- larly as classical inference relation is truth-preserving, forcing inference relation is preserving the level of inconsistency. The aim of the paper is to discuss some examples of inconsistent sets of premises, which can be analyzed by the use of Jennings-Schotch’s inference method. We will give simplified, with respect to its original formulation, versions of elementary notions needed to define the forcing relation. We also give examples of the use of this inference relation.