First Steps Towards Taming Description Logics with Strings

Abstract

We consider the description logic ALCF P pDΣq over the concrete domain DΣ " pΣ ˚, ă, ", p"wq wPΣ ˚q, where ă is the strict prefix order over finite strings in Σ ˚. Using an automata-based approach, we show that the concept satisfiability problem w.r.t. general TBoxes for ALCF P pDΣq is ExpTime-complete for all finite alphabets Σ. As far as we know, this is the first complexity result for an expressive description logic with a nontrivial concrete domain on strings.‹ The second author is supported by the Deutsche Forschungsgemeinschaft (DFG), project 504343613.