The Complexity of Modellability in Finite and Computable Signatures of a Constraint Logic for Head-Driven Phrase Structure Grammar

The SRL (speciate re-entrant logic) of King 1989] is a sound, complete and decidable logic designed speciically to support formalisms for the HPSG (head-driven phrase structure grammar) of Pollard and Sag 1994]. The SRL notion of modellability in a signature is particularly important for HPSG, and the present paper modiies an elegant method due to Blackburn and Spaan 1993] in order to prove that modellability in each computable signature is 0 1 , modellability in some nite signature is 0 1-hard (hence not decidable), and modellability in some nite signature is decidable. Since each nite signature is a computable signature, we conclude that 0 1-completeness is the least upper bound on the complexity of modellability both in nite signatures and in computable signatures, though not a lower bound in either.