Physical Systems as Constructive Logics

This paper is an investigation of S. Wolfram’s Principle of Computational Equivalence’ – that (discrete) systems in the natural world should be thought of as performing computations. We take a logical approach, and demonstrate that under almost trivial (physically reasonable) assumptions, discrete evolving physical systems give a class of logical models. Moreover, these models are of intuitionistic, or constructive logics – that is, exactly those logics with a natural computational interpretation under the Curry-Howard ‘proofs as programs’ isomorphism.