Title :   Conditional Event Algebras and Conditional Probability Logics. Basic Formulations and a Product Space Approach to Conditional Events.

Descriptive Note : Professional paper,

Corporate Author : NAVAL COMMAND CONTROL AND OCEAN SURVEILLANCE CENTER RDT AND E DIV SAN DIEGO CA

Personal Author(s) : Calabrese, Philip G. ; Goodman, I. R.

Report Date : NOV 1995

Pagination or Media Count : 38

Abstract : Part 1 reports the somewhat mutually inconsistent treatments of 'if-then-' by logic and probability is recounted and used to motivate a formal axiomatic development of conditional propositions in terms of partially-defined measurable characteristic functions on a sample space. The characteristic function of a conditional proposition (a/b), a given b, indicates for each instance w in the sample space whether (1) (a/b) applies and is true for a), or (2) (a/b) applies and is false for w, or (3) (a/b) is inapplicable since b is false. Four 3-valued truth tables characterize the 'and', 'or', 'not' and 'if-then-' operations of this algebra and capture the third truth state of 'inapplicable' for conditional propositions. This leads to an extension of the fundamental theorem of boolean algebra to conditional propositions. Finally. a set of four 4-valued truth tables is offered as a candidate for capturing both the "inapplicable" and "unknown" truth states. Part 2 reports some of the key issues giving rise to conditional event algebras. A rigorous formulation of the basic problem is presented together with a listing of natural properties which such conditional event algebras may be expected to satisfy. Most approaches to the issue have treated conditional events as-in effect-as generalized types of boolean functions. A review is presented of the two leading candidate algebras proposed by each of those authors. However, despite a number of desirable properties these enjoy, there are several difficulties that also occur, including formulation of higher order conditioning, modeling of independent information, and formulation of conditional random variables. (AN)

Descriptors :   *PROBABILITY, *MATHEMATICAL LOGIC, *EXPERT SYSTEMS, DATA BASES, MATHEMATICAL MODELS, PROBABILITY DISTRIBUTION FUNCTIONS, RANDOM VARIABLES, STATISTICAL INFERENCE, ALGEBRA, FUZZY SETS, DATA FUSION, OPERATORS(MATHEMATICS), SPECIAL FUNCTIONS(MATHEMATICS), MAPPING(TRANSFORMATIONS), FORMULAS(MATHEMATICS), BOOLEAN ALGEBRA.

Subject Categories : Statistics and Probability
Cybernetics
Theoretical Mathematics

Distribution Statement : APPROVED FOR PUBLIC RELEASE