Generating Explicit Orderings for Non-monotonic Logics

James Cussens, Anthony Hunter, Ashwin Srinivasan

For non-monotonic reasoning, explicit orderings over formulae offer an important solution to problems such as 'multiple extensions’ . However, a criticism of such a solution is that it is not clear, in general, from where the orderings should be obtained. Here we show how orderings can be derived from statistical information about the domain which the formulae cover. For this we provide an overview of prioritized logics-a general class of logics that incorporate explicit orderings over formulae. This class of logics has been shown elsewhere to capture a wide variety of proof-theoretic approaches to non-monotonic reasoning, and in particular, to highlight the role of preferences-both implicit and explicit-in such proof theory. We take one particular prioritized logic, called SF logic, and describe an experimental approach for comparing this logic with an important example of a logic that does not use explicit orderings of preference-namely Horn clause logic with negation-as-failure. Finally, we present the results of this comparison, showing how SF logic is more skeptical and more accurate than negation-as-failure.

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