发表机构
NIKI – Digital Engineering; TWT Science & Innovation（尼基数字工程公司; TWT科学与创新公司）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
本文围绕语义场理论展开，重构其演变并赋予清晰数学核心。核心方法是通过词汇表征等建模语言组织层次，贡献五个形式元素。主要贡献是为计算语言学等提供了可评估的模型及相关理论元素，虽非完整理论，但有重要意义。
AI 中文摘要
语义场理论（SFT）已从对语言游戏的强烈反形式主义解读的哲学批判发展成为一种用于词汇语义、高阶组合和稳定解释的计算模型类。本文重构了这一演变，并赋予SFT一个更清晰的数学核心，适用于计算语言学和表示学习中的独立评估。核心提议是通过表示为语义场的词汇表征、这些场的上下文变形、在令牌子集上定义的交互项以及由语义能量动力学控制的稳定化来对可处理的语言组织层次进行建模。本文贡献了五个形式元素。首先，定义了语义场模型。其次，证明了高斯积闭包结果。第三，通过在子集格上使用莫比乌斯反演推广了三字问题。第四，引入了阶谱。第五，将稳定解释表述为与句子相关的能量泛函的最小化并给出相关条件。一个小示例展示了三字组“夏日”如何用高斯语义场表示、在Python中实现并由流程图总结。结果并非自然语言意义的完整理论，也不能取代语言的社会、语用或规范解释。
英文摘要
Semantic Field Theory (SFT) has developed from a philosophical critique of strong anti-formalist readings of language games into a proposed computational model class for lexical semantics, higher order composition, and stabilized interpretation. This paper reconstructs that evolution and gives SFT a sharper mathematical core suitable for independent evaluation in computational linguistics and representation learning. The central proposal is that a tractable level of linguistic organization can be modeled through lexical representations expressed as semantic fields, through contextual deformation of those fields, through interaction terms defined over subsets of tokens, and through stabilization governed by semantic energy dynamics. The paper contributes five formal elements. First, it defines a semantic field model as a tuple consisting of a semantic space, a lexical field lifting, a contextual deformation map, an interaction complex, and an interpretation functional. Second, it proves a Gaussian product closure result showing that multiplicative field interactions have explicit centers, precisions, and compatibility factors. Third, it generalizes the three-word problem by using Mobius inversion on the subset lattice to isolate irreducible semantic interactions of arbitrary order. Fourth, it introduces an order spectrum that measures how much field mass is explained at each interaction order. Fifth, it formulates stabilized interpretation as minimization of an energy functional associated with the sentence and gives existence, descent, and stability conditions. A small worked example shows how a three-word summer day triple can be represented by Gaussian semantic fields, implemented in Python, and summarized by a flow diagram. The result is not a completed theory of natural language meaning and does not replace social, pragmatic, or normative accounts of language.
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