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Departmental Technical Reports (CS)

Product of Partially Ordered Sets (Posets), with Potential Applications to Uncertainty Logic and Space-Time Geometry

Francisco Zapata, The University of Texas at El Paso
Olga Kosheleva, The University of Texas at El PasoFollow
Karen Villaverde, New Mexico State University - Main CampusFollow

Publication Date

6-2011

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Technical Report: UTEP-CS-11-28

Published in International Journal of Innovative Management, Information & Production (IJIMIP), 2011, Vol. 2, No. 4, pp. 10-28.

Abstract

One of the main objectives of science and engineering is to help people select the most beneficial decisions. To make these decisions,

we must know people's preferences,
we must have the information about different events -- possible consequences of different decisions, and
since information is never absolutely accurate and precise, we must also have information about the degree of certainty.

All these types of information naturally lead to partial orders:

For preferences, a < b means that b is preferable to a. This relation is used in decision theory.
For events, a < b means that a can influence b. This causality relation is used in space-time physics.
For uncertain statements, a < b means that a is less certain than b. This relation is used in logics describing uncertainty such as fuzzy logic.

In many practical situations, we are analyzing a complex system that consists of several subsystems. Each subsystem can be described as a separate ordered space. To get a description of the system as a whole, we must therefore combine these ordered spaces into a single space that describes the whole system.

In this paper, we consider the general problem of how to combine two ordered spaces A and B into one. We also analyze which properties of orders are preserved under the resulting products.

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