Light Affine Set Theory: A Naive Set Theory of Polynomial Time
 Kazushige Terui
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In [7], a naive set theory is introduced based on a polynomial time logical system, Light Linear Logic (LLL). Although it is reasonably claimed that the set theory inherits the intrinsically polytime character from the underlying logic LLL, the discussion there is largely informal, and a formal justification of the claim is not provided sufficiently. Moreover, the syntax is quite complicated in that it is based on a nontraditional hybrid sequent calculus which is required for formulating LLL.
In this paper, we consider a naive set theory based on Intuitionistic Light Affine Logic (ILAL), a simplification of LLL introduced by [1], and call it Light Affine Set Theory (LAST). The simplicity of LAST allows us to rigorously verify its polytime character. In particular, we prove that a function over {0, 1}* is computable in polynomial time if and only if it is provably total in LAST.
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 Title
 Light Affine Set Theory: A Naive Set Theory of Polynomial Time
 Journal

Studia Logica
Volume 77, Issue 1 , pp 940
 Cover Date
 20040601
 DOI
 10.1023/B:STUD.0000034183.33333.6f
 Print ISSN
 00393215
 Online ISSN
 15728730
 Publisher
 Kluwer Academic Publishers
 Additional Links
 Topics
 Keywords

 naive set theory
 polynomial time
 linear logic
 light logic
 substructural logics
 Authors

 Kazushige Terui ^{(1)}
 Author Affiliations

 1. National Institute of Informatics, 212 Hitotsubashi, Chiyodaku, Tokyo, 1018430, Japan