粗糙性理论的列氏总分学分析

A Lesniewski Mereological Analysis on Roughness Theory

本文从探究粗糙总分学起源的上下文开始,回顾了其本源列氏总分学及其扩展后的塔氏立体几何关键内容。通过使用上述基本理论的术语和概念,对粗糙包含定义的公设系统进行了初步分析,从而阐述了对粗糙总分学的基本内涵理解。粗糙总分学体现了列氏总分学与粗糙性理论结合的一个方面,但列氏总分学作为与经典集合论相提并论的理论体系,具有完全基于该理论构造粗糙性的能力。基于此观点,本文首先描述了以集合论中划分的概念表达的粗糙集理论的形成原理,然后以列氏总分学概念来对等地替代集合论概念,以获得纯粹总分学意义上的粗糙性。这些思想和努力的最终目的,是利用总分学作为形式本体论要素的特质,建立作为软计算基本方法的粗糙性理论和作为知识/智能系统核心的本体论之间的关系,从而构建适应新型计算模式的方法学。

The present paper is set up to explore the context from which the Roug Mereology derives,mainly focusing on the original Mereology of Lesniewski and extension of Mereology to Tarski＇s Geometry of Solids. By using the notions from above fundamental theories,we take a naive analysis on the axiom system for Rough Inclusion definitions so as to clarify its connotation, Rough Mereology is an approach to combination of Mereology with Roughness Theory, but as a theory on par with respect to classical Set Theory, it is capable to build up the notion of Roughness purely over Mereology. Based on such intuition, the motivation that leads to roughness is first investigated in terms of classic set partitioning,and then transformed in the context of Mereology to attain a pure Mereological approach to roughness. It is the ultimate purpose of the present efforts that the essential role of Mereology in relation to Formal Ontology may bridge the methodology in Soft Computing to the key component in Knowledge/Intelligent System, say the Roughness Theory and the Formal Ontology, so as to construct new methodologies and theories to adapt emerging intelligent computing paradigm.