Nonmonotonicity and the scope of reasoning

Circumscription, default logic, and autoepistemic logic capture aspects of the nonmonotonicity of human commonsense reasoning. However, Perlis has shown that circumscription suffers from certain counterintuitive limitations, concerning exceptions or "counterexamples" to defaults. We observe that the unfortunate limitations of circumscription are even broader than Perlis originally pointed out. Moreover, these limitations are not peculiar to circumscription; they appear to be endemic in nonmonotonic reasoning formalisms. We develop a general solution, involving restricting the scope of nonmonotonic reasoning, and show that it remedies these problems in a variety of formalisms. Our solution has a number of attractive aspects in addition to its generality. Most importantly, no modification of the underlying formalisms is required, and the result is semantically compatible with existing approaches. Furthermore, the necessary machinery is intuitively plausible and, arguably, useful for other purposes. Finally, the solution is robust: it is relatively tolerant of imprecise determinations of scope.