The logic of interactive Turing reduction
Logic in Computer Science
2011-04-15 v4 Artificial Intelligence
Logic
Abstract
The paper gives a soundness and completeness proof for the implicative fragment of intuitionistic calculus with respect to the semantics of computability logic, which understands intuitionistic implication as interactive algorithmic reduction. This concept -- more precisely, the associated concept of reducibility -- is a generalization of Turing reducibility from the traditional, input/output sorts of problems to computational tasks of arbitrary degrees of interactivity. See http://www.cis.upenn.edu/~giorgi/cl.html for a comprehensive online source on computability logic.
Cite
@article{arxiv.cs/0512100,
title = {The logic of interactive Turing reduction},
author = {Giorgi Japaridze},
journal= {arXiv preprint arXiv:cs/0512100},
year = {2011}
}