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Fusions are a simple way of combining logics. For normal modal logics, fusions have been investigated in detail. In particular, it is known that, under certain conditions, de-cidability transfers from the component logics to their fusion. Though description logics are closely related to modal logics, they are not necessarily normal. In addition, ABox… (More)

We consider the monodic formulas of common knowledge predicate logic, which allow applications of epistemic operators to formulas with at most one free variable. We provide nite axiomatizations of the monodic fragment of the most important common knowledge predicate logics (the full logics are known to be not recursively enumerable) and single out a number… (More)

We investigate the expressive power and computational properties of two different types of languages intended for speaking about distances. First, we consider a first-order language FM the two-variable fragment of which turns out to be undecidable in the class of distance spaces validating the triangular inequality as well as in the class of all metric… (More)

In this paper we present a tableau calculus for a temporal extension of the description logic ALC, called T L ALC. This logic is based on the temporal language with`Until' interpreted over the natural numbers with expanding ALC-domains. The tableau calculus forms an elaborated combination of Wolper's tableau calculus for propositional linear temporal logic,… (More)

- Holger Sturm, Frank Wolter
- 2001

The aim of this paper is to construct a tableau decision algorithm for the modal description logic KALC with constant domains. More precisely , we present a tableau procedure that is capable of deciding, given an ALC-formula ' with extra modal operators (which are applied only to concepts and TBox axioms, but not to roles), whether ' is satiss-able in a… (More)

We introduce a family of languages intended for representing knowledge and reasoning about metric (and more general distance) spaces. While the simplest language can speak only about distances between individual objects and Boolean relations between sets, the more expressive ones are capable of capturing notions such as`somewhere in (or somewhere out of)… (More)

In [8, 6] we introduced a family of 'modal' languages intended for talking about distances. These languages are interpreted in 'distance spaces' which satisfy some (or all) of the standard axioms of metric spaces. Among other things, we singled out decidable logics of distance spaces and proved expressive completeness results relating classical and modal… (More)

1 Motivation and outline In order to ensure a reasonable and predictable behaviour of a Description Logic (DL) system, reasoning in the DL employed by the system should at least be decidable, and preferably of low complexity. Consequently, the expressive power of the DL in question must be restricted in an appropriate way. If the imposed restrictions are… (More)