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**An inequality paradigm for probabilistic knowledge. The logic of conditional probability intervals.**
*(English)*
Zbl 0608.68076

Uncertainty in artificial intelligence, Workshop Los Angeles/Calif. 1985, Mach. Intell. Pattern Recognition 4, 259-275 (1986).

[For the entire collection see Zbl 0595.00024.]

We propose an inequality paradigm for probabilistic reasoning based on a logic of upper and lower bounds on conditional probabilities. We investigate a family of probabilistic logics, generalizing the work of N. J. Nilsson [Artif. Intell. 28, 71-87 (1986; Zbl 0589.03007)]. We develop a variety of logical notions for probabilistic reasoning, including soundness; completeness; 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 Dempster-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.

We propose an inequality paradigm for probabilistic reasoning based on a logic of upper and lower bounds on conditional probabilities. We investigate a family of probabilistic logics, generalizing the work of N. J. Nilsson [Artif. Intell. 28, 71-87 (1986; Zbl 0589.03007)]. We develop a variety of logical notions for probabilistic reasoning, including soundness; completeness; 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 Dempster-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.

### MSC:

68T99 | Artificial intelligence |

03B48 | Probability and inductive logic |

60A05 | Axioms; other general questions in probability |