Non-standard logics for diagram interpretation

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    A key component of computational diagrammatic reasoning is the automated interpretation of diagram notations. One common and successful approach to this is based on attributed multiset grammars. The disadvantages of grammars are, however, that they do not allow ready integration of semantic information and that the underlying theory is not strongly developed. Therefore, embeddings of grammars into first-order logic have been investigated. Unfortunately, these are unsatisfactory: Either they are complex and unnatural or else, because of the monotonicity of classical first-order logic, cannot handle diagrammatic reasoning. We investigate the use of two non-standard logics, namely linear logic and situation theory, for the formalization of diagram interpretation and reasoning. The chief advantage of linear logic is that it is a resource-oriented logic, which renders the embedding of grammars straightforward. Situation theory, on the other hand, has been designed for capturing the semantics of natural language and offers powerful methods for modelling more complex aspects of language, such as incomplete views of the world. The paper illustrates embeddings of grammar-based interpretation into both formalisms and also discusses their integration.
    Original languageEnglish
    Title of host publicationTheory and Application of Diagrams
    Subtitle of host publicationFirst International Conference, Diagrams 2000 Edinburgh, Scotland, UK, September 1-3, 2000 Proceedings
    EditorsMichael Anderson, Peter Cheng, Volker Haarslev
    Place of PublicationBerlin Germany
    Number of pages16
    ISBN (Print)3540679154
    Publication statusPublished - 2000
    EventInternational Conference on the Theory and Application of Diagrams 2000 - Edinburgh, United Kingdom
    Duration: 1 Sep 20003 Sep 2000
    Conference number: 1st (Proceedings)

    Publication series

    NameLecture Notes in Computer Science
    ISSN (Print)0302-9743


    ConferenceInternational Conference on the Theory and Application of Diagrams 2000
    Abbreviated titleDiagrams 2000
    Country/TerritoryUnited Kingdom
    Internet address

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