Diagrammatic Reasoning with Classes and Relationships

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Abstract

We present and discuss a diagrammatic visualization and reasoning language coming about by augmenting Euler diagrams with higraphs. The diagrams serve (hierarchical as well as trans-hierarchical) classification and specification of various logical relationships between classes. The diagrams rely on a well-defined underlying class-relationship logic, called CRL, being a fragment of predicate logic. The inference rules at the level of diagrams take form of simple diagrammatic ipso facto rules. The diagrams are intended for computerization by offering navigation and zooming facilities as known from road maps. As such they may facilitate ontological engineering, which often involves larger amounts of data. The underlying inference process is expressible in function-free definite clauses, datalog. We also discuss the relationship to similar diagram and logic proposals.
Original languageEnglish
Title of host publicationVisual Reasoning with Diagrams
EditorsAmirouche Moktefi, Sun-Joo Shin
PublisherSpringer
Publication date2013
Pages83-100
ISBN (Print)978-3-0348-0600-8
DOIs
Publication statusPublished - 2013
SeriesStudies in Universal Logic

Keywords

  • Logic diagrams
  • Diagrammatic reasoning
  • Relationships between classes
  • Logical visualization principles and tools

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