Other logics that can be translated into GF2 include nominal tense logics and intuitionistic logic. This extends a previous result of the first author for grammar logics without converse. A consequence of the translation is that the general satisfiability problem for every regular grammar logics with converse is in EXPTIME. The class of regular grammar logics includes numerous logics from various application domains. It is practically relevant because it makes it possible to use a decision procedure for the guarded fragment in order to decide regular grammar logics with converse. The translation is theoretically interesting because it translates modal logics with certain frame conditions into first-order logic, without explicitly expressing the frame conditions. We provide a simple translation of the satisfiability problem for regular grammar logics with converse into GF2, which is the intersection of the guarded fragment and the 2-variable fragment of first-order logic. 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." "June 2005." Thesis (Ph. We improved the standard relational translation of modal logics, so that more modal logics can be translated into the guarded fragment. Building on this, we also studied translations from modal logics into the guarded fragment. We obtained a resolution-based decision procedure for the 2-variable fragment with equality. We obtained resolution decision procedures for the guarded fragment with and without equality. We have studied several aspects related to the use of resolution as decision procedure. In many cases, resolution can be modified in such a way that it becomes a decision procedure for certain subclasses of first-order logic. It is complete, but it does not terminate in general, when there exists no proof. Resolution is a well-known technique for first-order theorem proving. Abstract: "This cumulative habilitation thesis is based on five papers related to resolution decision procedures.
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