Jon Barwise and Lawrence S. Moss CSLI, 1996 Library of Congress QA248.B376 1996 | Dewey Decimal 511.322
The subject of non-wellfounded sets came to prominence with the 1988 publication of Peter Aczel's book on the subject. Since then, a number of researchers in widely differing fields have used non-wellfounded sets (also called "hypersets") in modeling many types of circular phenomena. The application areas range from knowledge representation and theoretical economics to the semantics of natural language and programming languages.
Vicious Circles offers an introduction to this fascinating and timely topic. Written as a book to learn from, theoretical points are always illustrated by examples from the applications and by exercises whose solutions are also presented. The text is suitable for use in a classroom, seminar, or for individual study.
In addition to presenting the basic material on hypersets and their applications, this volume thoroughly develops the mathematics behind solving systems of set equations, greatest fixed points, coinduction, and corecursion. Much of this material has not appeared before. The application chapters also contain new material on modal logic and new explorations of paradoxes from semantics and game theory.
This volume explores various problems in the syntax of Austronesian languages, which are found primarily in Malaysia and the Polynesian islands. Using the framework of constraint-based theories of syntax, contributors discuss the nature of these voice systems, the function of their verbal morphology, valence, verbal diathesis and transitivity in such languages, and the nature of their lexical categories. Each analysis is presented within the frameworks of lexical-functional grammar and head-driven phrase structure grammar.