Conditional Inference and Logic for Intelligent Systems: A Theory of Measure-free ConditioningThis work is concerned with addressing an anomoly involving probability and logic. This includes the interpretation and evaluation of implicative statements in natural language, compatible with conditional probability. One of the chief motivations for investigating this problem has been the need to formalize rigorously the appropriate connections between conditional probabilities and the underlying production rules in expert sytems. This is accomplished through the development of a comprehensive theory of conditional events and an associated logic. The results of this effort should be of prime use in the design and evaluation of inference rules in expert systems, and also, allow for a new expansion of probability to include at the syntactic level the concept of conditioning. The monograph is intended for two audiences: AI researchers who are primarily interested in the management of uncertainty in expert systems, and mathematicians in the fields of probabilistic modeling, logic, and algebra. |
Contents
CONTENTS | 5 |
A SURVEY OF PREVIOUS WORK ON CONDITIONAL EVENTS | 13 |
Chapter 2 | 43 |
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a'b v c'd a₂ abcd Adams algebraic structure axioms basic belief function binary operation Boolean algebra Boolean ring c'd v bd Calabrese Chapter classical two-valued logic commutative concept conditional Boolean polynomial conditional events conditional logic conditional probability conditional probability logic consider copula corresponding cosets cosets of principal defined denoted disjunction element entailment relation equivalent example extended finite fuzzy conditionals fuzzy logic fuzzy sets given Hailperin homomorphism idempotent indicator function isomorphism lattice Lemma logical operations Lukasiewicz's material implication mathematical maximal filter measure-free conditioning MV-algebra non-monotonic one-to-one operations on R|R P(ab P(alb partial order principal ideals probabilistic probability measure problem Proof properties quotient ring R/Rb random set regular rings satisfies Schay Schay's Section 3.4 semantic Sobocinski's Stone algebra subsets Theorem three-valued logic Triviality Result truth tables truth values uncertainty measures