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.


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: http://w210.ub.uni-tuebingen.de/dbt/volltexte/2004/1203/. Following this link, you will also find additional document information.

Electronically available file formats (451 pages):

Bibtex entry:

  author  = {Frank Richter},
  title   = {A Mathematical Formalism for Linguistic Theories
             with an Application in Head-Driven Phrase Structure
  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