Ordered E-Resolution and Path Logics

Ordering reenements are particularly useful for avoiding unnecessary search and for obtaining resolution decision procedures. This paper presents a general framework for ordered E-resolution, allowing arbitrary selection of negative literals and providing a general notion of redundancy elimination. As diierent theories bring forth diierent and very special simpliication rules, having an im-built general scheme for eliminating redundancy is especially useful. The strength of the framework is demonstrated for certain path logics arising by the optimised functional translation method from serial propositional modal logics.