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  1. Ontologies for Plane, Polygonal Mereotopology.Ian Pratt & Oliver Lemon - 1997 - Notre Dame Journal of Formal Logic 38 (2):225-245.
    Several authors have suggested that a more parsimonious and conceptually elegant treatment of everyday mereological and topological reasoning can be obtained by adopting a spatial ontology in which regions, not points, are the primitive entities. This paper challenges this suggestion for mereotopological reasoning in two-dimensional space. Our strategy is to define a mereotopological language together with a familiar, point-based interpretation. It is proposed that, to be practically useful, any alternative region-based spatial ontology must support the same sentences in our language (...)
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  • On the Insufficiency of Linear Diagrams for Syllogisms.Oliver Lemon & Ian Pratt - 1998 - Notre Dame Journal of Formal Logic 39 (4):573-580.
    In Volume 33:1 of the Notre Dame Journal of Formal Logic, a system for diagramming syllogistic inferences using straight line segments is presented by Englebretsen. In light of recent research on the representational power of diagrammatic representation systems by the authors, we point out some problems with the proposal, and indeed, with any proposal for representing logically possible situations diagrammatically. We shall first outline the proposed linear diagrammatic system of Englebretsen, and then show by means of counterexamples that it is (...)
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