An Algebraic Approach to Conditioning in Probability with Applications to the Combination of Evidence Problem.
Abstract
This presentation considers a fundamental problem touching upon four major disciplines: probability theory, boolean algebra and logic, ring theory, and the modeling of natural and formal language in expert systems. Specifically, this lecture treats the problem of annexing a conditional event operator to boolean algebra-as originally proposed by Boole and long neglected in the standard semantically oriented literature-which is compatible with all conditional probability evaluations, and which allows for the development of a full calculus of extended boolean operations and relations. In this lecture a new procedure is presented for dealing with the combination of such implicational statements, derived from a minimum of assumptions. This yields a sound and complete logic-conditional probability logic of propositions-which has connections with Koopman's qualitative conditional probability and possesses the algebraic structure of semi-boolean algebra. Extensive applications to use in expert systems are also exhibited, showing how this new approach to conditioning can be used in design of knowledge-based systems and the treatment of uncertainty factors.
Document Details
- Document Type
- Technical Report
- Publication Date
- Aug 01, 1991
- Accession Number
- ADA240879
Entities
People
- I. R. Goodman