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

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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 Π 01

  • modellability in some finite signature is Π 01 -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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Authors and Affiliations

  1. Seminar für Sprachwissenschaft, Eberhard-Karls-Universität, Kl, Wilhelmstr. 113, 72074, Tübingen, Germany

    Paul John King & Bjørn Aldag

  2. Laboratory for Linguistic Modelling, Bulgarian Academy of Sciences, Avenue Acad. G. Bonchev, Sofia, Bulgaria

    Kiril Ivanov Simov

Authors
  1. Paul John King
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  2. Kiril Ivanov Simov
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  3. Bjørn Aldag
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King, P.J., Simov, K.I. & Aldag, B. The Complexity of Modellability in Finite and Computable Signatures of a Constraint Logic for Head-Driven Phrase Structure Grammar. Journal of Logic, Language and Information 8, 83–110 (1999). https://doi.org/10.1023/A:1008247127922

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