Towards Theory of Massive-Parallel Proofs. Cellular Automata Approach

TL;DR

This paper proposes a novel theory of massively parallel proofs using cellular automata, eliminating axioms and enabling cyclic proofs within unconventional computing.

Contribution

It introduces a new approach to deduction theory based on cellular automata, avoiding axioms and supporting cyclic proofs.

Findings

First theory of massive-parallel proofs in unconventional computing

Cellular automata as local transition functions for inference

Supports cyclic proofs without additional issues

Abstract

In the paper I sketch a theory of massively parallel proofs using cellular automata presentation of deduction. In this presentation inference rules play the role of cellular-automatic local transition functions. In this approach we completely avoid axioms as necessary notion of deduction theory and therefore we can use cyclic proofs without additional problems. As a result, a theory of massive-parallel proofs within unconventional computing is proposed for the first time.