4 found
  1.  8
    Ian Pratt & Dominik Schoop (1998). A Complete Axiom System for Polygonal Mereotopology of the Real Plane. Journal of Philosophical Logic 27 (6):621-658.
    This paper presents a calculus for mereotopological reasoning in which two-dimensional spatial regions are treated as primitive entities. A first order predicate language ℒ with a distinguished unary predicate c(x), function-symbols +, · and - and constants 0 and 1 is defined. An interpretation ℜ for ℒ is provided in which polygonal open subsets of the real plane serve as elements of the domain. Under this interpretation the predicate c(x) is read as 'region x is connected' and the function-symbols and (...)
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  2.  8
    Ian Pratt & Dominik Schoop (2000). Expressivity in Polygonal, Plane Mereotopology. Journal of Symbolic Logic 65 (2):822-838.
    In recent years, there has been renewed interest in the development of formal languages for describing mereological (part-whole) and topological relationships between objects in space. Typically, the non-logical primitives of these languages are properties and relations such as `x is connected' or `x is a part of y', and the entities over which their variables range are, accordingly, not points, but regions: spatial entities other than regions are admitted, if at all, only as logical constructs of regions. This paper considers (...)
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    Panu Raatikainen, Ian Pratt, Dominik Schoop & A. Complete Axiom (1998). Maria Concetta di Maio and Alberto Zanardo. Journal of Philosophical Logic 27:659-660.
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    Ian Pratt-Hartmann & Dominik Schoop (2002). Elementary Polyhedral Mereotopology. Journal of Philosophical Logic 31 (5):469-498.
    A region-based model of physical space is one in which the primitive spatial entities are regions, rather than points, and in which the primitive spatial relations take regions, rather than points, as their relata. Historically, the most intensively investigated region-based models are those whose primitive relations are topological in character; and the study of the topology of physical space from a region-based perspective has come to be called mereotopology. This paper concentrates on a mereotopological formalism originally introduced by Whitehead, which (...)
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