用数学公理自动生成可追溯的证明，实现确定性推理与知识生成。
Generative Logic: A New Computer Architecture for Deterministic Reasoning and Knowledge Generation
- 基于公理系统构建分布式逻辑块，通过哈希推理引擎自动推导新定理。
- 在普通硬件上1分钟内完成核心证明，10分钟内完整运行并生成带溯源的证明图。
- 适合需要可验证推理的领域，如形式化验证、自动定理证明和可信AI。
我们提出生成逻辑（Generative Logic, GL），一种从用户提供的公理定义出发，系统探索其可配置演绎邻域的确定性架构。公理以极简数学编程语言（MPL）书写，编译为分布式的逻辑块（LB），通过统一的哈希推理引擎通信；当规则前提匹配时，即生成带有完整溯源的新事实，形成可重放、可审计的证明图。该流程包含孵化器（Incubator）自动生成基础事实表、压缩器（Compressor）消除证明后冗余，并由独立外部验证器完成34,320次检查，零失败。在初等数论实验中，从皮亚诺公理自主推导高斯求和公式。核心证明流水线在商品级硬件上不到1分钟完成，含孵化器的事实生成总计约10分钟。孵化器输出显示，GL可执行具体数值计算——每项结果均为带溯源的已证定理，为全溯源计算机代数系统（CAS）开辟路径。生成的证明可导出为可导航的HTML供独立审查。代码、证明图及复现说明见github.com/Generative-Logic/GL（commit 6e5b9a4），并存档于doi:10.5281/zenodo.17206386。
原文摘要 · Abstract (English)
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. Definitions are compiled into a distributed grid of Logic Blocks (LBs) that communicate via a unified hash-based inference engine; whenever the premises of a rule unify, a new fact is emitted with full provenance, yielding replayable, auditable proof graphs. The pipeline includes an Incubator that auto-generates ground-level fact tables, a Compressor that eliminates post-proof redundancy, and an independent external Verifier (34,320 checks, zero failures). Experimental validation on Elementary Number Theory develops Peano arithmetic from axioms and autonomously derives Gauss's summation formula. On commodity hardware, the core proving pipeline completes in under one minute; the full run including Incubator fact generation finishes in approximately ten minutes. The Incubator output further reveals that GL can perform concrete numerical calculations -- each result a proved theorem with full provenance -- opening a path toward a full-provenance Computer Algebra System (CAS). Generated proofs export as navigable HTML for independent inspection. Code, proof graphs, and reproduction instructions are available at github.com/Generative-Logic/GL (commit 6e5b9a4) and archived at doi:10.5281/zenodo.17206386.
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