We present L o g A G , a weighted algebraic non-monotonic logic for reasoning with graded beliefs. L o g A G is algebraic in that it is a language of only terms, some of which denote propositions and may be associated with ordered grades. The grades could be taken to represent a wide variety of phenomena including preference degrees, priority levels, trust ranks, and uncertainty measures. Reasoning in L o g A G is non-monotonic and may give rise to contradictions. Belief revision is, hence, an integral part of reasoning and is guided by the grades. This yields a quite expressive language providing an interesting alternative to the currently existing approaches to non-monotonicity. We show how L o g A G can be utilised for modelling resource-bounded reasoning; simulating inconclusive reasoning with circular, liar-like sentences; and reasoning about information arriving over a chain of sources each with a different degree of trust. While there certainly are accounts in the literature for each of these issues, we are not aware of any single framework that accounts for them all like L o g A G does. We also show how L o g A G captures a wide variety of non-monotonic logical formalisms. As such, L o g A G is a unifying framework for non-monotonicity which is flexible enough to admit a wide array of potential uses.

中文翻译：

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LogAG：用于对分级命题进行推理的代数非单调逻辑

我们提出了 Log AG，这是一种用于分级信念推理的加权代数非单调逻辑。Log AG 是代数的，因为它是一种只有术语的语言，其中一些表示命题并且可能与有序等级相关联。等级可以用来代表各种各样的现象，包括偏好程度、优先级、信任等级和不确定性度量。Log AG 中的推理是非单调的，可能会引起矛盾。因此，信念修正是推理的一个组成部分，并以成绩为指导。这产生了一种非常有表现力的语言，为当前存在的非单调性方法提供了一个有趣的替代方案。我们展示了如何利用 Log AG 对资源有界推理进行建模；用类似骗子的循环语句模拟不确定的推理；以及对通过不同信任度的来源链到达的信息进行推理。虽然在文献中肯定对这些问题中的每一个都有说明，但我们不知道有任何单一的框架可以像 Log AG 那样解决所有问题。我们还展示了 Log AG 如何捕获各种非单调逻辑形式。因此，Log AG 是一个非单调性的统一框架，它足够灵活以适应广泛的潜在用途。