Building Intelligent Databases Through Similarity: Interaction of Logical and Qualitative Reasoning

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 <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">$\Xi_{\mathcal{P}}$</tex> for each knowledge <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">$\mathcal{K}$</tex>, offering a nuanced approach to understanding and quantifying similarity. By defining the similarity knowledge space <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">$\Xi_{\mathcal{K}}$</tex> 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 <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">$\Xi_{\mathcal{K}}$</tex> 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.