Daily Arxiv

This page organizes papers related to artificial intelligence published around the world.
This page is summarized using Google Gemini and is operated on a non-profit basis.
The copyright of the paper belongs to the author and the relevant institution. When sharing, simply cite the source.

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

Created by
  • Haebom

Author

Nikolai Sergeev

Generative Logic (GL)

Outline

This paper presents Generative Logic (GL), a deterministic architecture that systematically explores the inference domain based on user-provided axiomatic definitions, along with optional facts written in a minimal mathematical programming language (MPL). Definitions are compiled into a distributed grid of simple Logic Blocks (LBs) that exchange messages. Whenever an inference rule's premises are matched, a new fact is generated, including full provenance information, resulting in a reproducible and auditable proof graph. A prototype software implementation instantiates the workflow in first-order Peano arithmetic. Starting from the Peano axioms, GL enumerates conjectures, applies normalization, types, and CE filters, and automatically reconstructs machine-verifiable proofs of fundamental arithmetic laws, including the associative and commutative laws of addition, the associative and commutative laws of multiplication, and the distributive law.

Takeaways, Limitations

Automatic generation of machine-verifiable proofs of the fundamental laws of Peano arithmetic.
All steps of the proof process can be reviewed.
Proposal of a hardware-software co-design path and the possibility of integration with probabilistic models.
Proof step execution time of approximately 7 seconds on commercial hardware.
Total running time: approximately 5 minutes.
GL focuses on a specific mathematical area (Peano arithmetic).
Hardware-software co-design is required for massively parallel implementation.
Integration with probabilistic models for automatic formatting and guess seeding is a future research topic.
👍