Formal theory of the comparative relations: its application to the study of quantum similarity and dissimilarity measures and indices

Abstract

The study proposes a formal theory of comparative relations characterized by a group of abstract definitions and axioms. This abstract characterization allows us to rigorously define in a very general form what a comparative relation is, which can in turn be used as starting point in every case where comparative analysis is used. Some of the consequences of this formalization—when applied to existing results- are analyzed, particularly those related with the consistency of the results of the comparisons. Following, a study was conducted of descriptors of Quantum Quantitative Structure–Property Relationships models proposed by Carbo-Dorca et al. Several quantum comparative indices such as: Carbo, Hodgkin–Richards, Petke, Tanimoto, conjugate Petke and conjugate Hodgkin–Richards were also analyzed. The proposed theory gives a solid theoretical basis for comparative analysis that will have a positive impact on a broad spectrum of disciplines, where the field of chemistry could be one of the most important beneficiaries.