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We give a new decision procedure for the guarded fragment with equality. The procedure is based on resolution with superposition. We argue that this method will be more useful in practice than methods based on the enumeration of certain finite structures. It is surprising to see that one does not need any sophisticated simplification and redundancy(More)
We provide a simple translation of the satisfiability problem for regular grammar logics with converse into GF, which is the intersection of the guarded fragment and the 2-variable fragment of first-order logic. This translation is theoretically interesting because it translates modal logics with certain frame conditions into first-order logic, without(More)
Recent years have seen considerable interest in procedures for computing finite models of first-order logic specifications. One of the major paradigms, MACE-style model building, is based on reducing model search to a sequence of propositional satisfiability problems and applying (efficient) SAT solvers to them. A problem with this method is that it does(More)
In this paper we give an overview of resolution methods for extended propositional modal logics. We adopt the standard translation approach and consider different resolution refinements which provide decision procedures for the resulting clause sets. Our procedures are based on ordered resolution and selection-based resolution. The logics that we cover are(More)
The guarded fragment is a fragment of first-order logic that has been introduced for two main reasons: First, to explain the good computational and logical behavior of propositional modal logics. Second, to serve as a breeding ground for well-behaved process logics. In this paper we give resolution-based decision procedures for the guarded fragment and for(More)
We provide a resolution-based proof procedure for modal and description logics that improves on previous proposals in a number of important ways. First, it avoids translations into large undecidable logics, and works directly on modal or description logic formulas instead. Second, by using labeled formulas it avoids the complexities of earlier propositional(More)
We prove the completeness of the combination of ordered resolution and factoring for a large class of non-liftable orderings, without the need for any additional rules like saturation. This is possible because of a new proof method wich avoids making use of the standard ordered lifting theorem. This proof method is based on resolution games. Resolution was(More)