概念代数的形式性质和规则

2015 IEEE 14th International Conference on Cognitive Informatics & Cognitive Computing (ICCI*CC) Pub Date : 2015-07-06 DOI:10.1109/ICCI-CC.2015.7259376

M. Valipour, Yingxu Wang

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引用次数: 8

摘要

概念代数是一种指称数学，用于在知识表示、语义分析和机器学习中严格操作形式概念及其代数运算。对概念代数的性质进行形式化的研究，以阐述形式化概念及其代数运算的本质。这导致了在形式概念上的关系、再生和组合操作范畴中的一组代数规则。严格描述了概念代数中代数运算之间的关系。用实例对概念代数的代数规则进行了证明。这项工作使概念代数在认知知识库操作和认知机器学习中的严格实现成为可能。

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Formal properties and rules of concept algebra

Concept algebra is a denotational mathematics for rigorously manipulating formal concepts and their algebraic operations in knowledge representation, semantic analyses, and machine learning. Properties of concept algebra are formally studied in order to elaborate the nature of formal concepts and their algebraic operations. This leads to a set of algebraic rules in the categories of relational, reproductive, and compositional operations on formal concepts. Relationship between algebraic operations of concept algebra is rigorously described. Proofs are provided for the algebraic rules of concept algebra elaborated by examples. This work enables a rigorous implementation of concept algebra in cognitive knowledge base manipulations and cognitive machine learning.

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2015 IEEE 14th International Conference on Cognitive Informatics & Cognitive Computing (ICCI*CC)

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