A new formal model of belief dynamics is proposed, in which the epistemic agent has both probabilistic beliefs and full beliefs. The agent has full belief in a proposition if and only if she considers the probability that it is false to be so close to zero that she chooses to disregard that probability. She treats such a proposition as having the probability 1, but, importantly, she is still willing and able to revise that probability assignment if she receives information that gives her sufficient reasons to do so. Such a proposition is (presently) undoubted, but not undoubtable (incorrigible). In the formal model it is assigned a probability 1 − δ , where δ is an infinitesimal number. The proposed model employs probabilistic belief states that contain several underlying probability functions representing alternative probabilistic states of the world. Furthermore, a distinction is made between update and revision, in the same way as in the literature on (dichotomous) belief change. The formal properties of the model are investigated, including properties relevant for learning from experience. The set of propositions whose probabilities are infinitesimally close to 1 forms a (logically closed) belief set. Operations that change the probabilistic belief state give rise to changes in this belief set, which have much in common with traditional operations of belief change.

中文翻译：

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修正概率和完全信念

提出了一种新的信念动态正式模型，其中认知代理同时具有概率信念和完全信念。当且仅当代理人认为错误的概率如此接近于零以至于她选择忽略该概率时，她才完全相信一个命题。她将这样的命题视为概率为 1，但重要的是，如果她收到的信息足以让她有理由这样做，她仍然愿意并且能够修改该概率分配。这样的命题（目前）是毋庸置疑的，但并非无可置疑（不可救药）。在正式模型中，它被分配了一个概率 1 − δ ，其中 δ 是一个无穷小的数。所提出的模型采用概率置信状态，其中包含几个代表世界的替代概率状态的潜在概率函数。此外，更新和修订之间有区别，就像在（二分）信念变化的文献中一样。研究了模型的形式属性，包括与从经验中学习相关的属性。概率无限接近 1 的命题集形成一个（逻辑上封闭的）信念集。改变概率信念状态的操作会引起这个信念集的变化，这与传统的信念变化操作有很多共同之处。研究了模型的形式属性，包括与从经验中学习相关的属性。概率无限接近 1 的命题集形成一个（逻辑上封闭的）信念集。改变概率信念状态的操作会引起这个信念集的变化，这与传统的信念变化操作有很多共同之处。研究了模型的形式属性，包括与从经验中学习相关的属性。概率无限接近 1 的命题集形成一个（逻辑上封闭的）信念集。改变概率信念状态的操作会引起这个信念集的变化，这与传统的信念变化操作有很多共同之处。