I have a long-standing personal and professional interest in language and how it works. As you read this page, please keep in my my personal bias. I like Sebastian Shaumyan's Applicative Universal Grammar (AUG). This page will be used to describe some interesting current efforts in the advancement of AUG and to distribute material useful in those efforts.
Applicative Universal Grammar is a semiotic theory of linguistics that uses combinatory logic (a higher order logic) as its formalism. The implications of a theory's being based on both semiotics and combinatory logic are far reaching. Applicative Universal Grammar can explain certain linguistic difficulties more eaily and more parsimoniously than can other linguistic theories. However, these benefits do not come without a price. Because of the substantial difference between first order and higher order logic, some techniques cannot be carried over from theories such as Generative Transformational Grammar to AUG. AUG theorists must think about linguistics from scratch.
Nancy Tinkman and I here at Rowan University are beginning a project that will extend work done at Yale University to build a computerized parser using AUG's principles and theory. As part of an international effort, the computer science department at Yale has built and distributes a functional programming language called HASKELL, named after Haskell Curry, the founder of combinatory logic. The preliminary parser work has been done in HASKELL. We will continue using HASKELL in our efforts.
Superposition is a theory in AUG that claims that, under certain circumstances, a linguistic expression can have a bistratal type as opposed to the simple types permitted by other linguistic theories. Because superposition is unique to AUG, the theory has not been explored by many linguists. Currently, my theoretical work has been almost entirely concerned with superposition and its implications.
The links below will get some papers that I have presented on aspects of superposition. I also post an extensive outline of Applicative Universal Grammar. This document is based on Professor Shaumyan's major work A Semiotic Theory of Language and several papers written since its publication.
To read these papers or the Outline of AUG, you will need the Adobe Acrobat Reader version 4.0. If you do not have a copy, you can obtain one free from Adobe's web site.
The following papers were presented at various LACUS Fora. The papers are made available by the kind permission of the Linguistic Association of Canada and the United States (LACUS) which is the copyright holder.
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