Compiling specificity into approaches to nonmonotonic reasoning

Abstract

We present a general approach for introducing specificity information into nonmonotonic theories. Historically, many approaches to nonmonotonic reasoning, including default logic, circumscription, and autoepistemic logic, do not provide an account of specificity, and so fail to enforce specificity among default sentences. In our approach, a default theory is initially given as a set of strict and defeasible rules. By making use of a theory of default conditionals, here given by System Z, we isolate minimal sets of defaults with specificity conflicts. From the specificity information intrinsic in these sets, a default theory in a target language is specified. For default logic the end result is a semi-normal default theory; in circumscription the end result is a set of abnormality propositions that, when circumscribed, yield a theory in which specificity information is appropriately handled. We mainly deal with default logic and circumscription although we also consider autoepistemic logic, Theorist, and variants of default logic and circumscription. This approach differs from previous work in that specificity information is obtained from information intrinsic in a set of conditionals, rather than assumed to exist a priori. Moreover, we deal with the “standard” version of, for example, default logic and circumscription and do not rely on prioritised versions, as do other approaches. The approach is both uniform and general, so the choice of the ultimate target language has little effect on the overall approach.