The Anti-Foundation Axiom In Constructive Set Theories (2003)
| Venue: | Stanford University Press |
| Citations: | 6 - 5 self |
BibTeX
@INPROCEEDINGS{Rathjen03theanti-foundation,
author = {M. Rathjen},
title = {The Anti-Foundation Axiom In Constructive Set Theories},
booktitle = {Stanford University Press},
year = {2003},
pages = {87--108},
publisher = {CSLI Publ}
}
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Abstract
. The paper investigates the strength of the antifoundation axiom on the basis of various systems of constructive set theories. 1. Introduction Intrinsically circular phenomena have come to the attention of researchers in differing fields such as mathematical logic, computer science, artificial intelligence, linguistics, cognitive science, and philosophy. Logicians first explored set theories whose universe contains what are called non-wellfounded sets, or hypersets (cf. [17], [5]). But the area was considered rather exotic until these theories were put to use in developing rigorous accounts of circular notions in computer science (cf. [7]). Instead of the Foundation Axiom these set theories adopt the so-called Anti-Foundation Axiom, AFA, which gives rise to a rich universe of sets. AFA provides an elegant tool for modeling all sorts of circular phenomena. The application areas range from knowledge representation and theoretical economics to the semantics of natural language and pr...
