A Theorem Prover for Prioritized Circumscription

In a recent paper, Ginsberg shows how a backward-chaining ATMS can be used to construct a theorem prover for circumscription. Here, this work is extended to handle prioritized circumscription. The ideas to be described have been implemented, and examples are given of the system in use. 1 Introduction Of all the approaches to nonmonotonic reasoning, Mc-Carthy's circumscription [McCarthy, 1980, McCarthy, 1986] seems to be the most popular. A great deal of work has gone into the development of new versions of circumscription designed to address various problems in commonsense reasoning. Much less work, however, has gone into the development of methods by which these formalisms might be implemented. In [Ginsberg, 1989], Ginsberg shows how a backward-chaining ATMS can be used to construct a theorem prover for circumscription. Here, this work is extended to handle prioritized circum-scription. In [Ginsberg, 1989], the following procedure is given to determine whether a particular sentence q follows from the circumscription axiom. First, you construct a default proof d for g, where d is a formula obtained by conjoining and disjoining instantiations of negations of the predicate being circumscribed. Then, you attempt to undermine this proof by constructing a default proof for ¬d. If you cannot undermine the original proof, then q is a consequence of the circumscription. This procedure implements parallel circumscription since all the defaults are treated equally. For almost all applications of nonmonotonic reasoning, however, it is necessary to establish a prioritization among the defaults. In inheritance hierarchies, for example, the general view is that defaults about a subclass should override defaults about its superclasses. So if Tweety is both a penguin and a bird, the default that penguins generally do not fly should have a higher priority than the default that birds generally do. In this paper, we show that the above method for computing parallel circumscription can be generalized to handle prioritized circumscription by extending the argument chain to consider arguments against the proposed proof of ¬d. One can view the procedure as a dispute between a believer B and an unbeliever U. B begins by presenting an argument for the desired conclusion. V then tries to rebut this argument by finding a counterargument at the same or higher priority. B now tries to refute the counterargument by finding a counter-counterargument at a strictly higher priority. This process of alternating rebuttals and refutations continues until one side cannot answer the other's …