Combining Terminological Logics with Tense Logic

We show how to add full first-order temporal expressiveness to terminological logics. This can be achieved by embedding point-based tense operators in propositionally closed concept languages like ALC. The resulting temporal terminological logics are fully expressive over linear, Dedekind complete time such as ℕ and ℝ in the sense that all first-order temporal formulae over these time structures are expressible. We then prove that augmenting ALC by future-oriented tense operators interpreted over linear, discrete, unbounded time like IN does not increase its computational complexity. To establish this complexity result we show that coherence in ALC augmented by functional roles and their transitive closure is computable in polynomial space. We finally show how to obtain directly an axiomatization and a tableau-based algorithm for the tenselogical extension of terminological logics.