FDE: A logic of clutters

Abstract

We uncover a ʼnaturally occurring’ first degree system, AL of Articular Logic that is both relevant and paraconsistent. The principal semantic innovation is an informationally articulated, but nevertheless entirely classical representation of wffs as clutters (Clutters are also referred to as simple hypergraphs in some contexts.) on the power set of a set of possible states. The principal methodological novelty is the general observation that distinct classical representations of wffs can be selected and combined with redeployments of classical inference to accommodate particular inferential requirements such as paraconsistency and relevance.