Articular models for first-degree paraconsistent systems

Abstract

We present a class of models (h-models) in which the sentences of a propositional language are represented as simple hypergraphs on the power set of a universe, and in which entailments are modeled by relations between hypergraphs. An h-model theoretic semantic analysis of the system FDE of first-degree entailment is proposed and a non-constructive completeness proof given in the familiar idiom of Henkin models. Finally we introduce a hitherto unstudied system of analytic entailment and provide its natural h-model representation.