Deduction and Search Strategies for Regular Multiple-Valued Logics

The inference rule !-resolution was introduced in [27] as a technique for developing an SLD-style query answering procedure for the logic programming subset of annotated logic. The inference rule requires that the lattice of truth values be ordinary. In this paper, it is proved that all complete distributive lattices are ordinary. Properties of !-resolution in the general theorem proving setting are explored, including the completeness of a variety of restrictions. It is shown that the pruning effects of classical restriction strategies (for example, ordering and the linear restriction) can be enhanced with the !-operator. Two macro inference rules, annotated hyperresolution and annotated hypertableaux, both of which can also be enhanced with the !-operator, are developed for annotated logics.