Using Resolution as Decision Procedure

This cumulative habilitation thesis is based on five papers related to resolution decision procedures. Resolution is a well-known technique for first-order theorem proving. It is complete, but it does not terminate in general, when there exists no proof. In many cases, resolution can be modified in such a way that it becomes a decision procedure for certain subclasses of first-order logic. We have studied several aspects related to the use of resolution as decision procedure. We obtained resolution decision procedures for the guarded fragment with and without equality. We obtained a resolution-based decision procedure for the 2-variable fragment with equality. Building on this, we also studied translations from modal logics into the guarded fragment. We improved the standard relational translation of modal logics, so that more modal logics can be translated into the guarded fragment. Finally, we showed that a standard refinement, using a liftable order, can be used to obtain a decison procedure for the E-class, which was an open problem.