Order Relations Are Ubiquitously Fundamental: Alexandrov(-Zeeman) Theorem Extended from Space-Time Physics to Logical Reasoning and Decision Making

Authors

Vladik Kreinovich, The University of Texas at El PasoFollow
Olga Kosheleva, The University of Texas at El PasoFollow
Laxman Bokati, The University of Texas at El PasoFollow
Laura Berrout, The University of Texas at El PasoFollow

Publication Date

5-1-2021

Comments

Technical Report: UTEP-CS-21-52

Abstract

In all areas of human activity, there are natural ordering relations: causality in space-time physics, preference in decision making, and logical inference in reasoning. In space-time physics, a 1950 theorem by A. D. Alexandrov proved that causality relation is fundamental: many other features, including numerical characteristics of time and space, can be reconstructed from this relation. In this paper, we provide simple proofs that, similarly, the corresponding ordering relations are fundamental in decision making and in logical reasoning.