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 - Tập 8 - Trang 83-110 - 1999
Paul John King1, Kiril Ivanov Simov2, Bjørn Aldag1
1Seminar für Sprachwissenschaft, Eberhard-Karls-Universität, Kl, Tübingen, Germany
2Laboratory for Linguistic Modelling, Bulgarian Academy of Sciences, Sofia, Bulgaria

Tóm tắt

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 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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Tài liệu tham khảo

Aldag, B., 1997, “A proof theoretic investigation of prediction in HPSG,” Master' Thesis, Seminar für Sprachwissenschaft, Eberhard-Karls-Universität, Tübingen, Germany.

van Benthem, J., 1984, “Correspondence theory,” pp. 167–247 in Handbook of Philosophical Logic, Volume II: Extensions of Classical Logic, D.M. Gabbay and F. Guenthner, eds., Synthese Library: Studies in Epistemology, Logic, Methodology, and Philosophy of Science, Vol. 165, Dordrecht: D. Reidel Publishing Company.

Berger, R., 1966, “The undecidability of the dominoe problem,” Memoirs of the American Mathematical Society 66, 1–72.

Blackburn, P. and Spaan, E., 1993, “A modal perspective on the computational complexity of attribute value grammar,” Journal of Logic, Language and Information 2, 129–169.

Enderton, H.B., 1977, “Elements of recursion theory,” pp. 527–566 in Handbook of Mathematical Logic, J. Barwise, ed., Studies in Logic and the Foundations of Mathematics, Vol. 90, Amsterdam: North-Holland Publishing Company.

Kasper, R.T. and Rounds, W.C., 1986, “A logical semantics for feature structures,” pp. 257–266 in Proceedings of the 24th Annual Meeting of the Association for Computational Linguistics, New York: New Work.

Kasper, R.T. and Rounds, W.C., 1990, “The logic of unification in grammar,” Linguistics and Philosophy 13, 35–58.

Kepser, S., “A satisfiability algorithm for a typed feature logic,” Master' Thesis, Seminar für Sprachwissenschaft, Eberhard-Karls-Universität, Tübingen, Germany.

King, P.J., 1989, “A logical formalism for head-driven phrase structure grammar,” Doctoral Thesis, Manchester University, Manchester, England.

King, P.J., 1994, “An expanded logical formalism for head-driven phrase structure grammar,” SFB 340 Technical Report, No. 59, Seminar für Sprachwissenschaft, Eberhard-Karls-Universität, Tübingen, Germany.

King, P.J. and Simov, K.Iv., 1997, “The automatic deduction of classificatory systems from finite linguistic theories,” in Grammars, in press.

Meurers, W.D. and Minnen, G., 1997, “A computational treatment of lexical rules in HPSG as covariation in lexical entries,” in Computational Linguistics 23(4).

Pollard, C.J., 1998, “Strong generative capacity in HPSG,” in Lexical and Constructional Aspects of Linguistic Explanation, G. Webelhuth, J.-P. Koenig, and A. Kathol, eds., Stanford, CA: CSLI Publications.

Pollard, C.J. and Sag, I.A., 1994, Head-Driven Phrase Structure Grammar, Chicago, IL: University of Chicago Press.

Richter, F. and Sailer, M., 1995, “Remarks on linearisation: Reflection on the treatment of LP-rules in HPSG in a typed feature logic,” Master' Thesis, Seminar für Sprachwissenschaft, Eberhard-Karls-Universität, Tübingen, Germany.

Robinson, R.M., 1971, “Undecidability and nonperiodicity for tilings of the plane,” Inventiones Mathematicae 12, 177–209.