关于数值确定三段论及相关片段复杂性的研究

关系三段论的逻辑

Logics for the Relational Syllogistic

本文针对亚里士多德三段论无法处理关系事实推理的问题，构建了关系三段论逻辑片段，探讨了归谬法的必要性，证明了三段论证明系统的存在性，并确定了所有片段的计算复杂度。

重新审视多级三段论的平均情况复杂度：从1995年Courant技术报告到Lean 4形式化

Revisiting average case complexity of multilevel syllogistic

本文通过Lean 4形式化，重新审视了多级三段论的平均情况复杂度，编码了Reischuk-Schindelhauer平均情况类、MLS/EMLS语义层、部分决策过程及其正确性证明，并推导了NP平均完全性和非AvP困难性推论。

Syllogisms in Rudimentary Linear Logic, Diagrammatically

We present a reading of the traditional syllogistics in a fragment of the propositional intuitionistic multiplicative linear logic and prove that with respect to a diagrammatic logical calculus that we introduced in a previous paper, a syllogism is provable in such a fragment if and only if it is diagrammatically provable. We extend this result to syllogistics with complemented terms à la De Morgan, with respect to a suitable extension of the diagrammatic reasoning system for the traditional case and a corresponding reading of such De Morgan style syllogistics in the previously referred to fra…

认知三段论：初步探索

Epistemic Syllogistic: First Steps

本文受自然逻辑启发，在认知语境下提出并研究模态三段论的若干变体，重点分析 de re 解释的认知必然三段论及其扩展，并给出若干公理化系统与完全性证明。

On the satisfiability problem for a 4-level quantified syllogistic and some applications to modal logic (extended version)

We introduce a multi-sorted stratified syllogistic, called 4LQSR, admitting variables of four sorts and a restricted form of quantification over variables of the first three sorts, and prove that it has a solvable satisfiability problem by showing that it enjoys a small model property. Then, we consider the fragments (4LQSR)^h of 4LQSR, consisting of 4LQSR-formulae whose quantifier prefixes have length bounded by h > 1 and satisfying certain syntactic constraints, and prove that each of them has an NP-complete satisfiability problem. Finally we show that the modal logic K45 can be expressed in…

自然语言推理的混合模型：以三段论逻辑为例

Hybrid Models for Natural Language Reasoning: The Case of Syllogistic Logic

针对LLMs在逻辑推理中组合性泛化不足的问题，提出结合符号推理与神经计算的混合架构，在确保完备性的同时实现高效推理。