A Problem Reduction Model for Non-Independent Subproblems

A hypergraph model is introduced, which besides including the AND/OR graph and slate space graph models as particulars, is adequate for problem solving tasks involving non independent subproblems. The hypergraph model is shown to be grounded on a nonstandard notion of conjunction such that the truth of a conjunction does not necessarily imply the truth of the conjuncts. A hypergraph search algorithm is given and shown to be equivalent to a resolution based theorem prover in a first order logic augmented with the special conjunction. A characterization is given of the class or problems requiring the full descriptive power of our mode!. The class includes problems involving resources, plan formation, simplification of predicate logic programs.