The principles underlying this paper can be applied not only to C2I systems, but also to many other complex structures, such as those involving medical, fault or configuration diagnoses and analyses. In short, a new relatively simple look-up table of formu

A Decision-Aid For Nodes in Command and Control Systems Based on

Cognitive Probability Logic

Dr. I.R. Goodman *

Code D44215, SPAWARSYSCEN,

San Diego, CA 92152-7446

Tel: 619-553-4014

Email: goodman@spawar.navy.mil

Abstract

The principles underlying this paper can be applied not only to C2I systems, but also to manyother complex structures, such as those involving medical, fault or configuration diagnoses andanalyses.

In short, a new relatively simple look-up table of formulas is presented which can be used as apractical aid in C2 decision-making nodes for deducing conditional or unconditional conclusionsfrom (conditional or unconditional) premises in probability form. This results from a recentbreakthrough yielding a new Cognitive Probability Logic -- or Logic of Averages. This logic isactually a natural weighting modification of Adams’ well-known High Probability Logic.Consequently, a number of long-standing conflicts between ordinary probability logic and“commonsense” reasoning are resolved for the first time, including the well-known transitivity-syllogism problem. These results are based upon completely rigorous universal second orderprobability principles, together with use of the newly emerging field of product spaceconditional event algebra. Surprisingly, both disciplines are actually technically entirely withinthe purview of classical logic and basic probability theory. Applications to linguistic-basedinformation can also be obtained by use of these techniques, together with one-point random setcoverage representations of fuzzy logic and an extension of product space conditional eventalgebra, dubbed relational event algebra.

1. Introduction

1.1 Overall Objectives

The chief thrust of this paper is to provide the basis for a new decision-aid in the form of arelatively simple look-up table of averaged probability values of conditional or unconditionalpotential deductions (or conclusions) that a C2 node decision maker may consider, given a finiteset of conditional or unconditional premises. However, as in many endeavors, it is equallyimportant to present both the skeletal derivation of certain of these results, and provide abackground on the controversy and progress involved in this area. Detailed proofs, as well asadditional important results, will be given in [Goodman & Nguyen, b].

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*This work was supported by the Office of Naval Research (ONR) In-House Laboratory Independent Research Program at SSC- SD, under FY99 IR Project No. ZU58.