Abstract
In this paper we present a computability and a complexity result on Relational Speciate Reentrant Logic (RSRL). RSRL is a description logic designed to formalise the linguistic framework and theory Head-Driven Phrase Structure Grammar. We show here that given an RSRL-formula and a finite RSRL-interpretation it is in general not decidable if the formula is true in the given interpretation by reduction to Post Correspondence Problems. For so-called chainless RSRL, a semantically weaker version in which the expressive power of RSRL is significantly reduced, we show that if a class of finite structures is definable in chainless RSRL it is decidable by a Turing machine polynomially time bounded in the size of the input structures.
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