Sections
1. Introduction
2. Sentential natural deduction
3. Generalizing to heterogeneous deduction
4. Generalizing to heterogeneous reasoning
5. Applications of the architecture
6. Conclusions and further work
7. Exercises and problems
8. References
Abstract
In this chapter, we describe a computational architecture for applications that support heterogeneous reasoning. Heterogeneous reasoning is, in its most general form, reasoning that employs representations drawn from multiple representational forms. Of particular importance, and the principal focus of this architecture, is heterogeneous reasoning that employs one or more forms of graphical representation, perhaps in combination with sentences (of English or another language, whether natural or scientific). Graphical representations include diagrams, pictures, layouts, blueprints, flowcharts, graphs, maps, tables, spreadsheets, animations, video, and 3D models. By “an application that supports heterogeneous reasoning” we mean an application that allows users to construct, record, edit, and replay a process of reasoning using multiple representations so that the structure of the reasoning is maintained and the informational dependencies and justifications of the individual steps of the reasoning can be recorded. Our architecture is based on the model of natural deduction in formal logic. In this chapter we describe and motivate the modifications to the standard logical model necessary to capture a wide range of heterogeneous reasoning tasks. The resulting generalization forms our computational architecture for heterogeneous reasoning (CAHR).