Applications of Abduction: An Inference Engine for Topovisual Qualitative Diagrammatic Reasoning

Qualitative Diagrammatic Reasoning Tim Menzies Department of Arti cial Intelligence, School of Computer Science and Engineering, University of New South Wales, Sydney, Australia, 2052 Phone: +61-2-9385-4034; Fax: +61-2-9385-5995; Email: [email protected]; URL: www.cse.unsw.edu.au/ timm May 9, 1997 Abstract Informal diagrams of theories are a common technique for illustrating and sharing expert intuitions. Normally, such theories are viewed as precursor to other modeling techniques which necessitates further analysis. Here we explore what semantics can be given to such diagrams without requiring further analysis. Given a diagram representing a theory, we characterise \understanding" a theory as a process of extracting a second explanation diagram from the theory diagram which is (i) permissive: it permits explanations of known/desired behaviour; (ii) restrictive: the explanatory diagram can be used to see what behaviour is impossible; (iii) comparable: we can judge the theory diagram relative to rival theories via an assessment of their possible explanation diagrams; (iv) re neable: we can recognise and cull useless portions of the theory diagram. This approach to diagrammatic reasoning is an inspired a new inference engine for qualitative diagrammatic non-physical problems where the problems are represented as topovisual graphs (not hypergraphs). We o er a formal abductive semantics for this style of constructive diagrammatic reasoning and discuss the limits of this technique.