经典语义地图模型求解的非唯一性问题

The Non-uniqueness of Classical Solutions of Semantic Map Models

语义地图模型是语言类型学中对跨语言的形义配对数据提取规律并进行可视化的一个方法,具体包含两个概念:概念空间反映跨语言普遍的各种功能在使用相同形式进行编码方面的倾向性分布;语义地图指单语中某具体语言形式的形式—功能配对。目前学者提出的方案大致可分为三类:基于图论的经典模型、加权图模型以及基于欧式空间的多维标度模型。在经典模型的求解过程中,由于需要遵守语义地图连通性假设,因此往往存在非唯一性问题(又称歧解问题),即根据给定数据,无法得到唯一确定的概念空间。后两种方法都将跨语言形义配对的频数信息纳入考虑,表面上规避了这一难题,但并未从根本上加以解决。本文将经典模型的求解看作最优化问题中的0-1规划,利用CPLEX软件求出所有可能的解。我们还将可能导致歧解的数据类型分为两类,分别对应分配式歧解和交替式歧解,并提出分配式歧解的一种表示方法——收缩法,可以将所有的歧解在一张图中展示出来。

The semantic map model is a research method in linguistic typology to extract generalizations and visualize them from cross-linguistic data of form-meaning pairs.It is composed of two notions,among which conceptual space reflects the co-encoding propensity of cross-linguistically universal functions,whereas semantic space refers to the form-meaning mapping of a specific linguistic form in one language.Thus so far three models have been proposed:the classical semantic map model,weighted semantic map model based on graph,and MDS model based on Euclidean space.In solving classical models,due to the existence of Semantic Map Connectivity Hypothesis,there always exists non-uniqueness.In other words,given data,one cannot have the only conceptual space as solution.The latter two avoid this problem by taking frequencies into consideration,yet they do not solve non-uniqueness by nature.This paper takes the classical model as a 0-1 integer programming in optimization problem and makes use of the software,CPLEX,to get all the solutions.We also classify the data types which cause non-uniqueness into two types corresponding to distributive and alternative ones respectively,and propose the contraction method as a visualization which can manifest all the distributive solutions in one graph.