Articular analysis

In this thesis I explore a new representational approach to relevance and paraconsistency. This approach is distinguished from truth-conditional, preservational and algebraic approaches in that it exploits the representation of inferentially significant structural features of sentences. The approach introduces a new hypergraphic idiom for the study of entailments. Historically the representation has roots in Leibnizian analyses, which, in an articular model, are represented as simple hypergraphs. The set of simple hypergraphs together with meet, join and complementation form a De Morgan lattice, in which the partial ordering is a relation called subsumption. One hypergraph subsumes another when every edge of the former finds a sub-edge in the other. The class of all such structures characterises a binary entailment system in which subsumption interprets entailment. Since a subsumption can itself be represented by a hypergraph, higher-degree systems also emerge with principles that depend solely upon properties of subsumption. In fact such systems arise for any theory of any item, including individuals, concepts, n-ary properties and so on, that are representable as hypergraphs. It follows, therefore, that a clear understanding of paraconsistent relations can be obtained between objects of many kinds.