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.Comment: To appear in Theoretical Computer Scienc