Building Intelligent Databases through Similarity: Interaction of Logical and Qualitative Reasoning
José-Luis Vilchis-Medina
TL;DR
This work addresses measuring similarity across knowledge domains within knowledge bases using a logic-based, qualitative framework. It introduces a similarity property space $Ξ_P$ and a similarity knowledge space $Ξ_K$ to capture context-dependent similarity between knowledge items, including a hierarchical organization via super-categories. The formalization defines three similarity classes $K'_{=}$, $K'_{ ough}$, and $K'_{ eq}$ (with $K'_{ ough}$ representing $\approx$), and shows how pairwise property relations $\mathcal{P}_{j}^{\mathcal{K}_{m}} / \mathcal{P}_{i}^{\mathcal{K}_{n}}$ populate $Ξ_P$, while $Ξ_K$ governs similarity source information. The framework is bounded to a finite number of categories, enabling structured, interpretable similarity analyses, though it raises questions about property selection subjectivity, dynamic knowledge, and uncertainty handling in real-world domains.
Abstract
In this article, we present a novel method for assessing the similarity of information within knowledge-bases using a logical point of view. This proposal introduces the concept of a similarity property space $Ξ$P for each knowledge K, offering a nuanced approach to understanding and quantifying similarity. By defining the similarity knowledge space $Ξ$K through its properties and incorporating similarity source information, the framework reinforces the idea that similarity is deeply rooted in the characteristics of the knowledge being compared. Inclusion of super-categories within the similarity knowledge space $Ξ$K allows for a hierarchical organization of knowledge, facilitating more sophisticated analysis and comparison. On the one hand, it provides a structured framework for organizing and understanding similarity. The existence of super-categories within this space further allows for hierarchical organization of knowledge, which can be particularly useful in complex domains. On the other hand, the finite nature of these categories might be restrictive in certain contexts, especially when dealing with evolving or highly nuanced forms of knowledge. Future research and applications of this framework focus on addressing its potential limitations, particularly in handling dynamic and highly specialized knowledge domains.