Light affine set theory: A naive set theory of polynomial time

Studia Logica 77 (1):9 - 40 (2004)
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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.

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Citations of this work

Routes to triviality.Susan Rogerson & Greg Restall - 2004 - Journal of Philosophical Logic 33 (4):421-436.
On arithmetic in the Cantor- Łukasiewicz fuzzy set theory.Petr Hájek - 2005 - Archive for Mathematical Logic 44 (6):763-782.
Paradoxes and contemporary logic.Andrea Cantini - 2008 - Stanford Encyclopedia of Philosophy.

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References found in this work

The lambda calculus: its syntax and semantics.Hendrik Pieter Barendregt - 1981 - New York, N.Y.: Sole distributors for the U.S.A. and Canada, Elsevier Science Pub. Co..
The undecidability of grisin's set theory.Andrea Cantini - 2003 - Studia Logica 74 (3):345 - 368.

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