概率知识的不等式范式
An Inequality Paradigm for Probabilistic Knowledge
摘要：
我们提出了一个不等式的概率推理的基础上的逻辑上的条件概率的上限和下限的范例。我们研究一族概率逻辑，推广了Nilsson的工作[14]。我们开发了各种逻辑概念的概率推理，包括健全性，完整性的理由;和收敛：减少一个理论到一个更简单的逻辑类。我们认为，一个绑定视图是特别有用的概率知识表示的语义描述和描述概率推理和更新的中间状态。我们表明，证据的Dempster-Shafer理论是正式相同的一个特殊情况下，我们的广义概率逻辑。因此，我们的范式结合了贝叶斯“基于规则”的方法和公开的非贝叶斯“证据”的方法，如MYCIN和DempsterShafer。我们建议如何整合这两个“学校”，并探讨了一些可能性，为新的综合各种想法的概率推理。
英文摘要：
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 Nilsson [14]. 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 bound 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 DempsterShafer. We suggest how to integrate the two "schools", and explore some possibilities for novel synthesis of a variety of ideas in probabilistic reasoning.
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