Combining knowledge representation and reasoning formalisms is an important and challenging task. It is important because non-trivial AI applications often comprise different aspects of the world, thus requiring suitable combinations of available formalisms modeling each of these aspects. It is challenging because the computational behavior of the resulting hybrids is often much worse than the behavior of their components. In this paper, we propose a new combination method which is computationally robust in the sense that the combination of decidable formalisms is again decidable, and which, nonetheless, allows non-trivial interactions between the combined components. The new method, called E-connection, is defined in terms of abstract description systems (ADSs), a common generalization of description logics, many logics of time and space, as well as modal and epistemic logics. The basic idea of E-connections is that the interpretation domains of n combined systems are disjoint, and that these domains are connected by means of n-ary ‘link relations. ’ We define several natural variants of E-connections and study in-depth the transfer of decidability from the component systems to their E-connections. Key words: description logics, temporal logics, spatial logics, combining logics, decidability.

Combining knowledge representation and reasoning formalisms like description logics (DLs), temporal logics, and logics of space, is worthwhile but difficult. It is worthwhile because usually application domains comprise various aspects of the world, thus requiring suitable combinations of formalisms modeling each of the aspects. It is difficult because the computational behavior of the resulting hybrids is often much worth than the behavior of it components. In this paper we propose a combination method which is robust in the computational sense and still allows for interactions between the combined systems. The combination method--called E-connection--will be defined and investigated for so-called abstract description systems (ADS) which subsume all standard description logics, various logics of time and space, modal logics, and epistemic logics. The main theoretical result is that the E-connection of any finite set of decidable ADSs is decidable as well. Four instances of E-connections of ADSs will be discussed: (1) The E-connection of DLs with the logic MS for quantitative reasoning about space, (2) the E-connection of DLs with the logic S4 u (containing RCC-8) for qualitative reasoning about space, (3) the E-connection of two DLs (ALCO and SHIQ), and (4) the E-connection of DLs with propositional temporal logic PTL and S4 u . 1 1