AN ANALYSIS OF 1ST-ORDER LOGICS OF PROBABILITY
AN ANALYSIS OF 1ST-ORDER LOGICS OF PROBABILITY
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DOI：
10.1016/0004-3702(90)90019-v
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发表时间：
1990-12-01
影响因子：
14.4
通讯作者：
HALPERN, JY
中科院分区：
文献类型：
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作者：
HALPERN, JY
我们考虑两种方法来赋予语义的概率的一阶逻辑。第一种方法将概率放在域上，并且适合于为涉及统计信息的公式提供语义，例如“随机选择的鸟飞行的概率大于0.9”。第二种方法在可能世界上放置概率，并且适合于为描述置信度的公式提供语义，例如“Tweety（特定鸟）飞行的概率大于0.9”。我们表明，这两种方法可以很容易地结合起来，使我们能够以一种简单的方式对统计信息和信仰程度的原因。然后，我们考虑公理化这些逻辑。一般来说，可以证明没有完全的公理化是可能的。我们提供的公理系统是健全的和完整的情况下，一个完整的公理化是可能的，表明它们确实允许我们捕捉大量有趣的推理概率。
We consider two approaches to giving semantics to first-order logics of probability. The first approach puts a probability on the domain, and is appropriate for giving semantics to formulas involving statistical information such as “The probability that a randomly chosen bird flies is greater than 0.9.” The second approach puts a probability on possible worlds, and is appropriate for giving semantics to formulas describing degrees of belief such as “The probability that Tweety (a particular bird) flies is greater than 0.9.” We show that the two approaches can be easily combined, allowing us to reason in a straightforward way about statistical information and degrees of belief. We then consider axiomatizing these logics. In general, it can be shown that no complete axiomatization is possible. We provide axiom systems that are sound and complete in cases where a complete axiomatization is possible, showing that they do allow us to capture a great deal of interesting reasoning about probability.