Nonmonotonic Reasoning and Defaults: On Rott’s Counterexamples

Author:Hao-Cheng Fu

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This paper aims to dissolve Rott’s counterexamples in terms of default logic proposed by Reiter in 1980. In his counterexample, Rott pointed out that some fundamental principles in AGM theory which meet the property of monotonicity are implausible because it seems unable to handle the processes of nonmonotonic reasoning which are common in our ordinary reasoning. In contrast to classical logic, AGM theory indeed developed a prominent way to deal with belief change, whereas many philosophers still casted doubts on the fundamental principles in AGM theory. For example, there might be some sentences in one’s belief set which are of the same form but different in information value and AGM theory does not commit it. Nevertheless, Rott failed to suggest a plausible way to fix the defect of AGM theory, so I aim to propose a suitable way to dissolve the problem of the processes of nonmontonic reasoning in virtue of the association of AGM theory with default logic.

Keywords: AGM theory、belief change、default logic、nonmontonic reasoning