揭示信念更新中反例与矛盾的互补作用，明确三类系统强弱关系。
Comparing Dialectical Systems: Contradiction and Counterexample in Belief Change (Extended Version)
- 通过形式化对比三类辩证系统，提出反例驱动更新更强
- 证明q系统严格强于p系统，后者又强于传统矛盾修正系统
- 为自动化推理与数学共同体信念演化提供统一框架
辩证系统是用于建模智能体在追求一致性过程中更新知识库的数学形式体系。自20世纪70年代由Roberto Magari提出以来，该框架最初旨在刻画数学家或研究共同体如何在探求真理过程中修正信念。如今，辩证系统也自然成为自动化代理信念更新的模型，提供了一种统一且可计算的动态信念管理框架。文献中主要区分三类：基于矛盾修正的(d-)辩证系统、基于发现反例修正的p-辩证系统，以及兼具二者能力的q-辩证系统。本文解决了文献中的一个开放问题，证明q-辩证系统严格强于p-辩证系统，而后者又严格强于(d-)辩证系统。这一结果凸显了反例与矛盾在自动化信念修正中的互补作用，进而揭示了数学家与研究共同体推理过程的本质特征。
原文摘要 · Abstract (English)
Dialectical systems are a mathematical formalism for modeling an agent updating a knowledge base seeking consistency. Introduced in the 1970s by Roberto Magari, they were originally conceived to capture how a working mathematician or a research community refines beliefs in the pursuit of truth. Dialectical systems also serve as natural models for the belief change of an automated agent, offering a unifying, computable framework for dynamic belief management. The literature distinguishes three main models of dialectical systems: (d-)dialectical systems based on revising beliefs when they are seen to be inconsistent, p-dialectical systems based on revising beliefs based on finding a counterexample, and q-dialectical systems which can do both. We answer an open problem in the literature by proving that q-dialectical systems are strictly more powerful than p-dialectical systems, which are themselves known to be strictly stronger than (d-)dialectical systems. This result highlights the complementary roles of counterexample and contradiction in automated belief revision, and thus also in the reasoning processes of mathematicians and research communities.
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