Abstract
The SRL (speciate re-entrant logic) of King (1989) is a sound, complete and decidable logic designed specifically 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 modifies an elegant method due to Blackburn and Spaan (1993) in order to prove that – modellability in each computable signature is Π01, – modellability in some finite signature is Π01-hard (hence not decidable), and – modellability in some finite signature is decidable. Since each finite signature is a computable signature, we conclude that Π01-completeness is the least upper bound on the complexity of modellability both in finite signatures and in computable signatures, though not a lower bound in either.
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