Reasoning with Analogical Representations

Abstract

Analogical representations have long been of interest to the knowledge representation community. Such representations provide compact encodings of information that can be cumbersome to represent and inefficient to manipulate in sentential languages. In this document, we address the problem of using analogical representations effectively in automated deduction systems. The primary contribution is a formal framework for combining analogical and deductive reasoning. The framework consists of a set of generic operations on analogical structures and accompanying inference methods for integrating analogical and sentential information. The capabilities of the framework are demonstrated for the task of reasoning to extend incomplete maps. The examples presented here have all been solved automatically by an implementation of the integration framework.