[论文解读] A Spin Glass Model of Human Logic Systems

Fariel Shafee|ArXiv.org|Sep 8, 2005

Computability, Logic, AI Algorithms参考文献 8被引用 8

一句话总结

本文提出一种自旋玻璃模型来表征人类逻辑系统，其中各主体基于高维世界中的对称性破缺，采用各不相同、依赖于感知的公理。通过相互作用，主体之间通过翻转机制影响彼此的公理，从而建模推理中的冲突；其主要贡献在于建立了一个正式框架，将哥德尔不完备性定理与社会网络中涌现的逻辑多样性联系起来。

ABSTRACT

In this paper, we discuss different models for human logic systems and describe a game with nature. Godel`s incompleteness theorem is taken into account to construct a model of logical networks based on axioms obtained by symmetry breaking. We start by saying that although an agent is rational, the axioms defining different agent's logic systems need not be the same although they might have a large degree of overlap. This can be seen as each agent being coupled to a higher dimensional world by means of his perception where the couplings produce slightly different projections of the higher dimensional world to each agent. The different projections would produce slightly different concepts about the "world" to each agent and hence create a slightly differing set of axioms that each agent would use to act logically. Then we place the agents in an interacting logical network, where these axioms can be treated as spins that can be flipped as agents interact with each other and with the environment in which they are placed. Agents, who would share a common material world that they wish to use or change by using different or conflicting sets of axioms will try to flip the other agent's axioms (This can be seen by observing that as one agent acts to interact with his world as followed by his axiom, another agent's world changes as well, and the change might be contradictory to the second agent's "axioms" or "optimal world". We define an equation that allows an axiom to be flipped into an "anti axiom (the opposite or conflicting axiom)" as agents interact. All agents share an "existence" axiom by means of which they strive to perpetuate themselves or the network.

研究动机与目标

• 将人类逻辑系统建模为非均匀的、依赖于感知的公理集合，其源于高维现实中的对称性破缺。
• 解释为何理性主体在共享物质世界的情况下仍可能持有相互冲突的逻辑框架。
• 将主体间的互动形式化为逻辑公理的动态翻转，以建模社会推理中的冲突与适应。
• 将哥德尔不完备性定理整合进社会系统中认知多样性的物理模型。
• 提出一种网络化逻辑系统，其中共享的存在公理维系主体的持续存在与相互作用。

提出的方法

• 公理由对高维世界的感知投影导出，从而形成主体特异的逻辑框架。
• 主体被建模为自旋玻璃系统中的自旋，每个自旋代表一个逻辑公理。
• 主体间的相互作用会引发公理向其相反形式（反公理）的翻转，代表逻辑冲突。
• 动态方程控制公理在互动过程中发生翻转的概率或可能性。
• 系统包含一个所有主体都力图维持的共享“存在”公理，以确保网络的稳定性。
• 通过承认任何单一逻辑系统都无法同时完备且一致，将哥德尔不完备性定理整合进该模型，从而为公理集合的多样性提供正当性。

实验结果

研究问题

• RQ1 为何具有不同逻辑框架的理性主体能在共享世界中共存而不产生矛盾？
• RQ2 何种机制使得逻辑公理能在社会互动中发生演化或翻转？
• RQ3 对高维现实的感知如何导致产生既发散又自洽的逻辑系统？
• RQ4 哥德尔不完备性定理以何种方式限制了任一单一逻辑系统在人类认知中的普遍性？
• RQ5 共享的存在公理在稳定具有冲突逻辑的主体网络中扮演何种角色？

主要发现

• 由于对高维现实的感知投影方式不同，不同主体发展出独特的逻辑系统。
• 公理并非普遍适用，而是源于对称性破缺，从而导致逻辑框架的固有多样性。
• 主体间的互动可导致某主体的公理翻转为其相反形式，从而建模推理或信念体系中的冲突。
• 共享的“存在”公理的存在确保了主体及网络的持续性，即使在逻辑冲突中亦然。
• 该模型为社会推理中认知多样性和冲突的涌现提供了一种类比——自旋玻璃动力学。