Light Affine Set Theory: A Naive Set Theory of Polynomial Time Article

DOI :
10.1023/B:STUD.0000034183.33333.6f

Cite this article as: Terui, K. Studia Logica (2004) 77: 9. doi:10.1023/B:STUD.0000034183.33333.6f
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Abstract 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 non-traditional 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 .

naive set theory polynomial time linear logic light logic substructural logics

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Authors and Affiliations 1. National Institute of Informatics, 2-1-2 Hitotsubashi Japan