Generative Logic: A Deterministic Reasoning Engine

arXiv:2508.00017v5 Announce Type: replace-cross Abstract: We present Generative Logic (GL), a deterministic computer architecture for automated mathematical reasoning. GL starts from axiomatic definitions written in a minimalist Mathematical Programming Language (MPL) and explores a configurable region of their deductive neighborhood. The definitions are compiled into a grid of Logic Blocks (LBs). An LB applies rules by hash-table lookups, and every statement it derives keeps its complete provenance. A run generates conjectures, removes those that counterexamples refute, tries to prove the rest, reduces the proved theorems to an essential core and writes every proof as navigable HTML. An independent verifier checks every proof step. From supplied definitions, GL derives the basic laws of Peano arithmetic and Gauss's summation formula. From previously proved lemmas, further definitions and a supplied list of conjectures, it builds a proof of the Fundamental Theorem of Arithmetic (FTA). These proofs are also exported to Lean 4 and checked by the Lean kernel. The next step is for GL to derive the FTA as well, without supplied conjectures. GL is designed together with a hardware architecture, the Mathematical Processing Unit (MPU).