Syntactic Conditional Closures for Defeasible Reasoning

An approach to nonmonotonic inference based on a closure operation on a conditional knowledge base is presented The central idea is that, given a theory of default conditionals, an extension to the theory le defined that satisfies certain intuitive restrictions Two notions for forming an extension are given, corresponding to the incorporation of irrelevant properties in conditionals and of transit ivity among condi tionals, in this approach these notions coincide Several equivalent definitions for an extension are developed general nonconstructive definitions, and a general "pseudo-iterative" definition Reasoning wi th irrelevant properties is correctly handled, as is specificity, reasoning within exceptional circumstances, and inheritance reasoning Tina approach is intented to ultimately serve as the proof-theoretic analogue to an extant semantic development based on preference orderings among possible worlds 1 I n t r o d u c t i o n A continuing problem in Arti f icial Intelligence is dealing with general, generic sentences that admit exceptions For example, suppose we are given that birds fly birds have wings, penguins are birds, and penguins don't fly We can write this in a propositional gloss as