Extending Semantic Resolution via Automated Model Building: Applications

An extension of semantic resolution is proposed. It is also an extension of the set of support as it can be considered as a particular case of semantic resolution. It is proved sound and refutationally complete. The extension is based on our former method for model building. The approach uses constrained clauses (or c-clauses), i.e. couples [clause : constraint]. Two important new features are introduced with respect to semantic resolution. Firstly, the method builds its own (finite or infinite) models to guide the search or to stop it if the initial set of clauses is satisfiable. Secondly, instead of evaluating a clause in an interpretation it imposes conditions (coded in its rules) to force a c-clause not to be evaluated to true in the interpretation it builds. The extension is limited in this paper to binary resolution but generalizing it to nary-resolution should be straightforward. The prover implementing our method is an extension of OTTER and compares advantageously with it (if binary resolution is used in OTTER), both in the search space and in the proof lenght of a relevant non trivial example. Last but not least, model building is incremental. This feature is specially useful when dealing with large set of clauses.