Guarded fixed-point logic μGF extends the guarded fragment by means of least and greatest fixed points, and thus plays the same role within the domain of guarded logics as the modal μ-calculus plays within the modal domain. We provide a semantic characterization of μGF within an appropriate fragment of second-order logic, in terms of invariance under guarded bisimulation. The corresponding characterization of the modal μ-calculus, due to Janin and Walukiewicz, is lifted from the modal to the guarded domain by means of model theoretic translations. Guarded second-order logic, the fragment of second-order logic which is introduced in the context of our characterization theorem, captures a natural and robust level of expressiveness with several equivalent characterizations. For a wide range of issues in guarded logics it may take up a role similar to that of monadic second-order in relation to modal logics. At the more general methodological level, the translations between the guarded and modal domains make the intuitive analogy between guarded and modal logics available as a tool in the further analysis of the model theory of guarded logics.

this paper, we generalise the principles from tableau algorithms for modal logics in order to develop a tableau algorithm for CGF. To the best of our knowledge, this is the rst algorithm for CGF that can be used as the basis for an ecient implementation

Guarded fixed point logic /spl mu/GF extends the guarded fragment by means of least and greatest fixed points, and thus plays the same role within the domain of guarded logics as the modal /spl mu/-calculus plays within the modal domain. We provide a semantic characterisation of /spl mu/GF within an appropriate fragment of second-order logic, in terms of invariance under guarded bisimulation. The corresponding characterisation of the modal /spl mu/-calculus, due to D. Janin and I. Walukiewicz (1999), is lifted from the modal to the guarded domain by means of model theoretic translations. At the methodological level, these translations make the intuitive analogy between modal and guarded logics available as a tool in the analysis of the guarded domain.

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 quantifierfree queries is computable in polynomial time, we show here that already for conjunctive queries, the reliability may become highly intractable. We exhibit a conjunctive query whose reliability problem is complete for FP #P . We further show, that FP #P is the typical complexity level for the reliability problems of a very large class of queries, including all second-order queries. We study approximation algorithms and prove that the reliabilities of all polynomial-time evaluable queries can be efficiently approximated by randomized algorithms. Finally we discuss the extension of our approach to the more general metafinite database model where finite relational structures are endowed with functions into an infinite interpreted domain; in addition queries may use aggregate ...