The New Directed Hypergraph for CNF Formula of Propositional Logic

Abstract

Propositional logic is a highly important formalism language in knowledge representation and automatic reasoning. In the present paper, directed hypergraph is a tool used to represent CNF formula and explore SAT problems. The directed hypergraph associated with CNF formula is constructed and the one-to-one correspondence between them is proved. Some equivalent results are analyzed the relationships of two clauses and directed hyperarcs. Due to B-graphs can't represent all Horn formulas directly, we define the extended B-graph associated with them and a new way to express hyperpath. The satisfiability of special cases of Horn formula is given.