A Mathematical Formalism for Linguistic Theories with an
Application in Head-Driven Phrase Structure Grammar
Frank Richter
Doctoral dissertation,
Eberhard-Karls-Universität Tübingen, June 23rd, 2000.
Published in 2004.
This is the final version of my dissertation.
It is almost identical with a previous
version circulated between summer 2000 and spring 2004
but it corrects a number of minor errors. Due to some reformating
in order to produce good PDF output, the page numbering is slightly
different.
Summary
This dissertation belongs in the field of mathematical
linguistics. It presents a logical formalism called Relational
Speciate Re-entrant Language (RSRL), which is suitable for specifying
with mathematical precision grammars which are written in the
framework of Head-Driven Phrase Structure Grammar (HPSG).
At the beginning two formalisms are presented which are based on
previous literature on the topic. These two formalisms reconstruct the
two versions of HPSG, both fundamentally different from a logical
point of view, which Carl Pollard and Ivan Sag described informally in
their books from 1987 and 1994. Because of deficiencies found in
previous mathematizations of the 1994 version of HPSG, this is
followed by the presentation of a new and much more comprehensive
formalism, RSRL, which is based on and extends the previous
formalisms. In this section the model theoretic properties of RSRL are
examined, and its relationship to previous explanations of the meaning
of HPSG grammars investigated. The appropriateness of RSRL for the
foremost task it is designed for is demonstrated finally by the
complete logical specification in RSRL of the HPSG grammar of English
from Pollard and Sag's 1994 book.
The last chapter reports new developments in HPSG which are already
based on RSRL. The appendices contain comprehensive presentations of
all necessary mathematical proofs.
My dissertation was electronically published on the publication server
of the University of Tübingen,
TOBIAS-lib. Its official location is on the publication server of
the university
library in Tübingen. Please cite this document quoting the
URL under which it is stored there:
https://publikationen.uni-tuebingen.de/xmlui/handle/10900/46230. Following
this link, you
will also find additional document information.
Electronically available file formats (451 pages):
Bibtex entry:
@phdthesis{richter:diss,
author = {Frank Richter},
title = {A Mathematical Formalism for Linguistic Theories
with an Application in Head-Driven Phrase Structure
Grammar},
type = {Phil. Dissertation (2000)},
school = {Eberhard-Karls-Universit{\"a}t T{\"u}bingen},
urlpage = {http://w210.ub.uni-tuebingen.de/dbt/volltexte/2004/1203/},
year = {2004}
}
Frank Richter
Last modified: Tue Aug 14 17:01:10 MEST 2001