From truth to computability I

Details From truth to computability I From truth to computability I

2004-07-21

arxiv.org/abs/cs/0407054v2

Theoretical Computer Science 357 (2006), pp. 100-135

Computer Science

Logic in Computer Science

To appear in Theoretical Computer Science

Scientific paper

10.1016/j.tcs.2006.03.014

The recently initiated approach called computability logic is a formal theory of interactive computation. See a comprehensive online source on the subject at http://www.cis.upenn.edu/~giorgi/cl.html . The present paper contains a soundness and completeness proof for the deductive system CL3 which axiomatizes the most basic first-order fragment of computability logic called the finite-depth, elementary-base fragment. Among the potential application areas for this result are the theory of interactive computation, constructive applied theories, knowledgebase systems, systems for resource-bound planning and action. This paper is self-contained as it reintroduces all relevant definitions as well as main motivations.

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