Argumentative consequence, non-monotony, and relevance

Abstract

The paper explores the particularities of argumentative consequence relation. Among its important characteristics are soundness (where sound argument is an argument that is both valid and has true premises) and defeasibility. The latter property suggests the possibility for argumentative reasoning to be defeated in the light of potential of criticism and/or additional information. Based on these considerations, a semantic interpretation of argumentative consequence relation is proposed as a kind of restriction of the classical one by the additional requirement for the set of premises to be satisfiable, which presupposes the existense of a truth-value assignment for the variables that makes all the premises true. This informally generated condition leads to defeasibility of the consequence relation. Adding arbitrary information to the original set of premises (either self-contradictory, or contradicting previously accepted premises) becomes prohibited. Hereinafter I propose a consequence system formalizing the introduced above concept of argumentative (semantic) consequence, and prove its semantic adequacy. This system in turn serves as a basis for further relevantization of the first degree semantic consequence relation enriched with an extra requirement for a conclusion to be non-tautological.