From truth to computability I

TL;DR

This paper proves soundness and completeness for a deductive system in computability logic, a formal framework for interactive computation, focusing on a basic first-order fragment with potential applications in various computational theories.

Contribution

It provides the first soundness and completeness proof for CL3, a key system in the foundational theory of computability logic, specifically for its elementary-base fragment.

Findings

Soundness and completeness of CL3 established

Formalization of the elementary-base fragment of computability logic

Potential applications in resource-bound planning and knowledge systems

Abstract

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.