arXiv cs.CL· Mehmet Murat Albayrako\u{g}lu·· 11 小时前AI 评分18
语义条件相似度（SCS）：一个形式化数学框架
Semantic Conditional Similarity (SCS): A Formal Mathematical Framework
AI 导读
论文提出语义条件相似度（SCS），在消除与第三份文档共享的语义元素后计算两份文档的相似度，通过集合论操作实现无需任意相似度阈值的共享与残余内容划分。SCS 引入方向性，将两两关系分为横向（源间）与纵向（源到目标）两类，并把比较域从无序对扩展到由目标、参考和条件文档组成的有序三元组。
正文 · 原文
Abstract:Semantic Textual Similarity (STS) operates on document pairs, returning a single scalar per comparison. In a multi-document setting where several sources may have contributed to one or more targets, pairwise STS cannot disentangle each source's marginal semantic contribution from their shared vocabulary. In this paper, Semantic Conditional Similarity (SCS) is introduced as a conditional form of STS that computes similarity between two documents after eliminating semantic elements shared with a third via set-theoretic operations. SCS makes four contributions: 1) it introduces directionality, partitioning pairwise relations into lateral (inter-source) and vertical (source-to-target) classes; 2) conditioning induces role-dependent asymmetry by extending the comparison domain from unordered pairs to ordered, conditioned triples of a target, a reference, and a conditioning document; 3) SCS introduces inter-document conditioning by subtracting shared content from a third document, complementing the intra-document conditioning in recent C-STS work; and 4) the set-theoretic decomposition achieves threshold-free partitioning of shared and residual content, requiring no arbitrary similarity cutoff. Although developed for the $n \to 1$ configuration, the framework extends to $1 \to n$ via vertical role reversal and to $m \to n$ via independent composition of source- and target-side conditioning. With the established $1 \to 1$ case, these span the full spectrum of document cardinality. SCS scores should be interpreted ordinally, as rankings of marginal contributions rather than absolute measurements. The broader implication is that metric space axioms commonly assumed in similarity formalizations constrain expressiveness in role-differentiated multi-document settings, and that extending the domain to conditioned triples can recover information that pairwise-symmetric comparisons suppress.
| Comments: | 34 pages, 6 figures, 8 tables, to be submitted for publication |
| Subjects: | Computation and Language (cs.CL) |
| MSC classes: | 68T50, 62H20, 62H30 |
| ACM classes: | H.3.3; I.2.7; I.5.2 |
| Cite as: | arXiv:2611.08778 [cs.CL] |
| (or arXiv:2611.08778v1 [cs.CL] for this version) | |
| https://doi.org/10.48550/arXiv.2611.08778 arXiv-issued DOI via DataCite (pending registration) |
Submission history
From: Mehmet Murat Albayrakoglu [view email]
[v1]
Thu, 5 Nov 2026 23:00:03 UTC (975 KB)
来源：arXiv cs.CL · arxiv.org