A MeasureFree Approach to Conditioning
I. Goodman
Abstract:
In an earlier paper, a new theory of measurefree "conditional" objects was presented. In this paper, emphasis is placed upon the motivation of the theory. The central part of this motivation is established through an example involving a knowledgebased system. In order to evaluate combination of evidence for this system, using observed data, auxiliary at tribute and diagnosis variables, and inference rules connecting them, one must first choose an appropriate algebraic logic description pair (ALDP): a formal language or syntax followed by a compatible logic or semantic evaluation (or model). Three common choices for this highly nonunique choice  are briefly discussed , the logics being Classical Logic, Fuzzy Logic, and Probability Logic. In all three,the key operator representing implication for the inference rules is interpreted as the oftenused disjunction of a negation ( b => a ) = (b'v a) , for any events a,b.
However, another reasonable interpretation of the implication operator is through the familiar form of probabilistic conditioning. But, it can be shown  quite surprisingly  that the ALDP corresponding to Probability Logic cannot be used as a rigorous basis for this interpretation! To fill this gap, a new ALDP is constructed consisting of "conditional objects", extending ordinary Probability Logic, and compatible with the desired conditional probability interpretation of inference rules. It is shown also that this choice of ALDP leads to feasible computations for the combination of evidence evaluation in the example. In addition, a number of basic properties of conditional objects and the resulting Conditional Probability Logic are given, including a characterization property and a developed calculus of relations.
Keywords:
Pages: 270277
PS Link:
PDF Link: /papers/87/p270goodman.pdf
BibTex:
@INPROCEEDINGS{Goodman87,
AUTHOR = "I. Goodman
",
TITLE = "A MeasureFree Approach to Conditioning",
BOOKTITLE = "Proceedings of the Third Conference Annual Conference on Uncertainty in Artificial Intelligence (UAI87)",
PUBLISHER = "AUAI Press",
ADDRESS = "Corvallis, Oregon",
YEAR = "1987",
PAGES = "270277"
}

