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Main web source on the subject: overview, downloadable articles, links.
site exerpt
COMPUTABILITY LOGIC: a theory of interactive computation HOMEPAGE  This material is based upon work supported by the National Science Foundation under Grant No. 0208816 What is Computability Logic? Potential applications of CL Papers on CL Links to related websites Abstracts What is Computability Logic? Computability is certainly one...
http://www.cis.upenn.edu/~giorgi/cl.html

Lecture notes for an undergraduate class taught by Leonid Levin at UC Berkeley.
http://www.cs.bu.edu/fac/lnd/toc/

Wikipedia article.
http://en.wikipedia.org/wiki/Church-Turing_thesis

Wikipedia article.
http://en.wikipedia.org/wiki/Computability_theory

Wikipedia article.
site exerpt
Interactive computation Wikipedia, the free encyclopedia  Interactive computation involves communication with the external world during the computation. This is in contrast to the traditional understanding of computation which assumes a simple interface between a computing agent and its environment, consisting in asking a question (input) and...
http://en.wikipedia.org/wiki/Interactive_computation

A directory of resources related to theoretical computer science from Stanford University.
http://ai.stanford.edu/~suresh/theory/theory-home.html