A Correspondence between Temporal Description Logics

Description Logics (DLs) are formalisms for representing and reasoning about conceptual knowledge. There exist several extensions of DLs for an appropriate integration of temporal knowledge [4]. This paper investigates the relation between the two DLs T L-ALCF [2, 3] and ALCF(D) [10, 8]. T L-ALCF is an interval-based, temporal DL for reasoning about objects whose properties vary over time. ALCF(D) is a logic for integrated reasoning about conceptual and so-called concrete knowledge. If instantiated with a \temporal" concrete domain, ALCF(D) is well-suited for reasoning about temporal objects, i.e., objects which have a unique temporal extension. This paper is a rst attempt to clarify the relationship between these two formalisms. It is showed that satis ability of T L-ALCF concepts can be reduced to satis ability of ALCF(D) concepts. This allows to use the available ALCF(D) tableau calculus for reasoning with T L-ALCF . Furthermore, it allows to settle the complexity of satis ability of T L-ALCF concepts, which was previously unknown. The paper is organized as follows. Sections 2 and 3 introduce the syntax and semantics of the two temporal DLs. In Section 4, a normal form for T L-ALCF concepts is introduced. Based on this normal form, the reduction of satis ability of T L-ALCF concepts to satis ability of ALCF(D) concepts is given.