Deduction and Inference Using Conditional Logic and Probability
Deduction and Inference Using Conditional Logic and Probability
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使用条件逻辑和概率进行演绎和推理
DOI：
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发表时间：
1991
期刊：
影响因子：
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通讯作者：
P. Calabrese
中科院分区：
文献类型：
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作者：
P. Calabrese
摘要：作者在1987年的论文中提出了一个条件逻辑和条件概率的代数合成，从命题的初始布尔代数开始，本文从事件的初始概率空间开始，并生成相关的命题作为可测量的指示函数（a la的方法B。De Finetti）。条件命题被生成为限制于正概率测度子集的可测指示函数。与、或、非和给定的运算是为任意条件命题定义的。结果的条件事件代数作为一个3值逻辑的表示（总是可能的，根据一个新的定理由于I。R. Goodman）是以三值真值表给出的。证明了（q/p）v（s/r）等复杂条件命题的条件概率公式。本文的第二个主题是关于条件命题领域的演绎。事实证明，根据所选择的特定蕴涵关系（<或+），条件命题有各种各样的逻辑推理。这些关系，包括他们的晶格性质和性质和性质的非单调性进行了探讨。人工智能的计算方面也进行了讨论。
Abstract : In contrast to the author's 1987 paper, which presented an algebraic synthesis of conditional logic and conditional probability starting with an initial Boolean algebra of propositions,this paper starts with an initial probability space of events and generates the associated propositions as measurable indicator functions (a la the approach of B. De Finetti). Conditional propositions are generated as measureable indicator functions restricted to subset of positive probability measure. The operations of and, or, not, and given are defined for arbitrary conditional propositions. The representation of the resulting conditional event algebra as a 3-valued logic (always possible according to a new theorem due to I. R. Goodman) is given in terms of 3-valued truth tables. Formulas for the conditional probability of complex conditional propositions such as (q/p) v (s/r) are proved. A second major theme of the paper concerns deductions in the realm of conditional propositions. It turns out that there are varieties of logical deduction for conditional propositions depending on the particular entailment relation (< or +) chosen. These relations are explored including their lattice properties and properties and properties of non-monotonicity. Computational aspects for Artificial Intelligence are also discussed.