A Paper Abstract by Benjamin Grosof

An Inequality Paradigm for Probabilistic Knowledge (1986)

by Benjamin N. Grosof

Abstract: We propose an inequality paradigm for probabilistic reasoning based on a a logic of upper and lower bounds on conditional probabilities. We investigate a family of probabilistic logics, generalizing the work of Nilsson. We develop a variety of logical notions for probabilistic reasoning, including soundness; completeness; and justification; and convergence: reduction of a theory to a simpler logical class. We argue that a bounds view is especially useful for describing the semantics of probabilistic knowledge representation and for describing intermediate states of probabilistic inference and updating. We show that the Dempter-Shafer theory of evidence is formally identical to a special case of our generalized probabilistic logic. Our paradigm thus incorporates both Bayesian "rule-based" approaches and avowedly non-Bayesian "evidential" approaches such as MYCIN and Dempster-Shafer. We suggest how to integrate the two "schools", and explore some possibilities for novel synthesis of a variety of ideas in probabilistic reasoning.
Last update: 1-8-98
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