Title

Inter-diagrammatic reasoning

Date of Completion

January 1997

Keywords

Artificial Intelligence|Computer Science

Degree

Ph.D.

Abstract

Although research in diagrammatic reasoning is as old as research in artificial intelligence itself, it has only recently aroused from a long dormancy induced by a bias toward symbolic computing. This resurgence of interest has been almost exclusively slanted towards the investigation of how a computer might be coaxed into generating information from isolated diagrams. In contrast, we examine how a computer might reason with groups of related diagrams inferring, for example, weather information from a suite of cartograms or the best move in a game from a sequence of diagrams delineating moves up to the current point. Diagrammatic reasoning research has rarely been conducted from this perspective and never with this distinction in mind. We contend that there are many diagrammatic domains that will prove amenable to this inter-diagrammatic perspective and that much can be learned about diagrammatic reasoning in general from such research. In particular, we (1) distinguish inter-diagrammatic and intra-diagrammatic reasoning, (2) define the syntax and semantics of a general diagram useful across a number of domains, (3) define a set of operators and functions that can effect inter-diagrammatic reasoning across a number of domains, (4) describe the formal properties of this set, and explore the relationship of this set with more traditional sets of operators, (5) codify the process by which a diagrammatic domain can be suitably defined to profit from these diagrammatic operators, (6) develop a variety of examples of inter-diagrammatic reasoning in a number of different domains including formal presentation and coding, (7) examine the possibility and utility of combining inter-diagrammatic reasoning with other AI reasoning paradigms, and (8) provide a selection of topics for further research in inter-diagrammatic reasoning. ^