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We provide a simple translation of the satisfiability problem for regular grammar logics with converse into GF 2 , 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)

We provide techniques to integrate resolution logic with equality in type theory. The results may be rendered as follows. − A clausification procedure in type theory, equipped with a correctness proof, all encoded using higher-order primitive recursion. − A novel representation of clauses in minimal logic such that the λ-representation of resolution steps… (More)

We present a proof procedure that is complete for first-order logic, but which can also be used when searching for finite models. The procedure uses a normal form which is based on geometric formulas. For this reason we call the procedure geometric resolution. We expect that the procedure can be used as an efficient proof search procedure for first-order… (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)

We give a new decision procedure for the guarded fragment with equality. The procedure is based on resolution with su-perposition. 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 resolution-based proof procedure for modal, description and hybrid logic that improves on previous proposals in important ways. It avoids translations into large undecidable logics, and works directly on modal, description or hybrid logic formulas instead. In addition, by using the hybrid machinery it avoids the complexities of earlier… (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)

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 proposi-tional 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 close the gap in complexity classification of the subsumption problem in the simple description logic FL 0 , which allows for conjunctions and universal value restriction only. We prove that subsumption in FL 0 is PSPACE-complete when cyclic definitions with descriptive semantics are allowed. Our proof uses automata theory and as a by-product the… (More)