Syntactic Conditional Closures for Defeasible Reasoning

Abstract

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 is 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 transitivity among conditionals; in this approach these notions coinci.de. Several equivalent definitions for an extenswn are developed: general nonconstructive definitions; and a general "pseudo-iterative" definition. Reasoning with irrelevant properties is correctly handled, as is specificity, reasoning within exceptional circumstances, and inheritance reasoning. This approach is intented to ultimately serve as the proof-theoretic ana logue to an extant semantic development based on preference orderings among possible worlds.