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- Egon Börger, Erich Grädel, Yuri Gurevich
- Perspectives in Mathematical Logic
- 1997

- Erich Grädel
- J. Symb. Log.
- 1999

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)

- Erich Grädel, Phokion G. Kolaitis, Moshe Y. Vardi
- Bulletin of Symbolic Logic
- 1997

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)

- Erich Grädel
- Theor. Comput. Sci.
- 1991

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)

- Achim Blumensath, Erich Grädel
- LICS
- 2000

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)

- Erich Grädel, Igor Walukiewicz
- LICS
- 1999

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)

- Achim Blumensath, Erich Grädel
- Theory of Computing Systems
- 2004

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)

- Erich Grädel, Martin Otto
- Theor. Comput. Sci.
- 1999

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)

- Erich Grädel, Yuri Gurevich, Colin Hirsch
- PODS
- 1998

The reliability of database queries on databases with uncertain information is studied, on the basis of a probabilistic model for unreliable databases. While it was already known that the reliability of quanti erfree queries is computable in polynomial time, we show here that already for conjunctive queries, the reliability may become highly intractable. We… (More)

- Erich Grädel, Martin Otto, Eric Rosen
- LICS
- 1997

w e prove that the satisfiability and the finite satisfiability problems for C2 are decidable. C2 is first-order logic with only two variables in the presence of arbitrary counting quantifiers 32", m 2 1. I t considerably extends L2, plain first-order with only two variables, which is known to be decidable by a result of Mortimer's. Unlike L2, C2 does not… (More)