Erich Grädel

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Guarded fragments of rst-order logic were recently introduced by Andr eka, van Benthem and N emeti; they consist of relational rst-order formulae whose quantiiers are appropriately relativized by atoms. These fragments are interesting because they extend in a natural way many propositional modal logics, because they have useful model-theoretic properties(More)
We identify the computational complexity of the satisfiability problem for FO, the fragment of first-order logic consisting of all relational first-order sentences with at most two distinct variables. Although this fragment was shown to be decidable a long time ago, the computational complexity of its decision problem has not been pinpointed so far. In 1975(More)
We investigate the expressive power of certain fragments of second-order logic on finite structures. The fragments are second-order Horn logic, second-order Krom logic as well as a symmetric and a deterministic version of the latter. It is shown that all these logics collapse to their existential fragments. In the presence of a successor relation they(More)
We study definability and complexity issues for automatic and ω-automatic structures. These are, in general, infinite structures but they can be finitely presented by a collection of automata. Moreover, they admit effective (in fact automatic) evaluation of all first-order queries. Therefore, automatic structures provide an interesting framework for(More)
Guarded fixed point logics are obtained by adding least and greatest fixed points to the guarded fragments of firstorder logic that were recently introduced by Andréka, van Benthem and Németi. Guarded fixed point logics can also be viewed as the natural common extensions of the modal -calculus and the guarded fragments. We prove that the satisfiability(More)
We study definability problems and algorithmic issues for infinite structures that are finitely presented. After a brief overview over different classes of finitely presentable structures, we focus on structures presented by automata or by model-theoretic interpretations. These two ways of presenting a structure are related. Indeed, a structure is automatic(More)
This paper is a survey and systematic presentation of decidability and complexity issues for modal and non-modal two-variable logics. A classical result due to Mortimer says that the two-variable fragment of rst-order logic, denoted FO 2 , has the nite model property and is therefore decidable for satissability. One of the reasons for the signiicance of(More)