Transformational Hierarchical Reasoning

Abstract

This paper presents a generalization of Robinson and Staples's window inference system of hierarchical reasoning. The generalization enhances window inference so that it is capable of supporting transformational proofs. In addition, while Robinson and Staples proposed window inference as an alternative to existing styles of reasoning, this paper describes window inference in terms of a sequent formulation of natural deduction. Expressing window inference in terms of natural deduction, a style of reasoning already known to be sound, demonstrates the soundness of window inference itself. It also illustrates how mechanized support for window inference can be implemented using existing sequent-based theorem provers. The paper also examines the use of contextual assumptions with window inference. Two definitions of what may be assumed in a context are presented. The first is a general definition; while the second has a simpler form. These definitions are shown to be equivalent for contexts that do not bind variables.