Generative Logic: A New Computer Architecture for Deterministic Reasoning and Knowledge Generation

Abstract

We present Generative Logic (GL), a deterministic architecture that starts from user-supplied axiomatic definitions, written in a minimalist Mathematical Programming Language (MPL), and systematically explores a configurable region of their deductive neighborhood. A defining feature of the architecture is its unified hash-based inference engine, which executes both algebraic manipulations and deterministic logical transformations. Definitions are compiled into a distributed grid of simple Logic Blocks (LBs) that exchange messages; whenever the premises of an inference rule unify, a new fact is emitted with full provenance to its sources, yielding replayable, auditable proof graphs. Experimental validation is performed on Elementary Number Theory (ENT) utilizing a batched execution strategy. Starting from foundational axioms and definitions, the system first develops first-order Peano arithmetic, which is subsequently applied to autonomously derive and prove Gauss's summation formula as a main result. To manage combinatorial explosion, GL algorithmically enumerates conjectures and applies normalization, type constraints, and counterexample (CE) filtering. On commodity hardware, an end-to-end run completes in under 7 minutes. Generated proofs export as navigable HTML so that every inference step can be inspected independently. We outline a hardware-software co-design path toward massively parallel realizations and describe future integration with large language models (LLMs) for auto-formalization and conjecture seeding. The Python, C++, and MPL code to reproduce these experiments, along with the full proof graphs in HTML as well as machine-readable text format, are available in the project's GitHub repository at github.com/Generative-Logic/GL commit 1771330 and are permanently archived at doi:10.5281/zenodo.17206386.