Connecting abstract description systems.
Oliver Kutz, Frank Wolter, and Michael Zakharyaschev
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 realistic application domains comprise various aspects of the world, thus requiring suitable combinations of formalisms modeling each of these aspects. It is difficult because the computational behavior of the resulting hybrids is often much worth than the behavior of its components. In this paper we propose a combination method which is robust in the computational sense and still allows for certain interactions between the combined systems. The combination method, called E-connection, will be defined and investigated for so-called abstract description systems (ADS) which include all standard description logics, various logics of time and space, modal logics, and epistemic logics. The main theoretical result is that every E-connection of any finite number 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 intended for quantitative reasoning about space, (2) the E-connection of DLs with the logic S4_u (containing RCC-8) that can be used 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.