A Proof-Theoretic Reconstruction of HPSG

Stephan Raaijmakers


Abstract
A reinterpretation of Head-Driven Phrase Structure Grammar (HPSG) in a proof-theoretic context is presented. This approach yields a decision procedure which can be used to establish whether certain strings are generated by a given HPSG grammar. It is possible to view HPSG as a fragment of linear logic (Girard, 1987), subject to partiality and side conditions on inference rules. This relates HPSG to several categorial logics (Morrill, 1990) . Specifically, HPSG signs are mapped onto quantified formulae, which can be interpreted as second-order types given the Curry-Howard isomorphism. The logic behind type inference will, aside from the usual quantifier introduction and elimination rules, consist of a partial logic for the undirected implication connective. It will be shown how this logical perspective can be turned into a parsing perspective. The enterprise takes the standard HPSG of Pollard – Sag (1987) as a starting point, since this version of HPSG is well-documented and has been around long enough to have displayed both merits and shortcomings; the approach is directly applicable to more recent versions of HPSG, however. In order to make the proof-theoretic recasting smooth, standard HPSG is reformulated in a binary format.
Anthology ID:
1993.iwpt-1.19
Volume:
Proceedings of the Third International Workshop on Parsing Technologies
Month:
August 10-13
Year:
1993
Address:
Tilburg, Netherlands and Durbuy, Belgium
Editors:
Harry Bunt, Robert Berwick, Ken Church, Aravind Joshi, Ronald Kaplan, Martin Kay, Bernard Lang, Makoto Nagao, Anton Nijholt, Mark Steedman, Henry Thompson, Masaru Tomita, K. Vijay-Shanker, Yorick Wilks, Kent Wittenburg
Venue:
IWPT
SIG:
SIGPARSE
Publisher:
Association for Computational Linguistics
Note:
Pages:
235–256
Language:
URL:
https://aclanthology.org/1993.iwpt-1.19
DOI:
Bibkey:
Cite (ACL):
Stephan Raaijmakers. 1993. A Proof-Theoretic Reconstruction of HPSG. In Proceedings of the Third International Workshop on Parsing Technologies, pages 235–256, Tilburg, Netherlands and Durbuy, Belgium. Association for Computational Linguistics.
Cite (Informal):
A Proof-Theoretic Reconstruction of HPSG (Raaijmakers, IWPT 1993)
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PDF:
https://preview.aclanthology.org/ingest-acl-2023-videos/1993.iwpt-1.19.pdf