Generative Logic: A New Computer Architecture for Deterministic Reasoning and Knowledge Generation
This work addresses the challenge of scalable, auditable automated theorem proving for foundational mathematics, with potential integration into broader AI systems, though it is incremental in applying existing logical methods to a new architecture.
The authors tackled the problem of deterministic reasoning and knowledge generation by introducing Generative Logic (GL), a new computer architecture that systematically explores deductive neighborhoods from axiomatic definitions, resulting in a prototype that automatically reconstructs machine-checkable proofs of foundational arithmetic laws in about 5 minutes on commodity hardware.
We present Generative Logic (GL), a deterministic architecture that starts from user-supplied axiomatic definitions (and, optionally, a list of simple facts for counterexample (CE) construction), written in a minimalist Mathematical Programming Language (MPL), and systematically explores their deductive neighborhood. 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. A prototype software implementation instantiates the workflow on first-order Peano arithmetic. Starting only from the Peano axioms, GL enumerates conjectures, applies normalization, type, and CE filter, and automatically reconstructs machine-checkable proofs of foundational arithmetic laws, including associativity and commutativity of addition, associativity and commutativity of multiplication, and distributivity. On commodity hardware, the prover phase requires approximately 7 seconds; a complete run finishes in about 5 minutes. Generated proofs export to 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 prospective integration with probabilistic models (e.g., large language models) for auto-formalization and conjecture seeding. The Python, C++, and MPL code to reproduce the Peano 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 56c9233 and are permanently archived at doi:10.5281/zenodo.17206386.