A complete axiom system for polygonal mereotopology of the real plane

Journal of Philosophical Logic 27 (6):621-658 (1998)
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 constants are given their meaning in terms of a Boolean algebra of polygons. We give an alternative interpretation base on the real closed plane which turns out to be isomorphic to ℜ. A set of axioms and a rule of inference are introduced. We prove the soundness and completeness of the calculus with respect to the given interpretation
Keywords mereology  spatial  reasoning  topology  logic
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DOI 10.1023/A:1004361501703
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Ian Pratt-Hartmann (2002). A Topological Constraint Language with Component Counting. Journal of Applied Non-Classical Logics 12 (3-4):441-467.
Stefano Borgo & Claudio Masolo (2010). Full Mereogeometries. Review of Symbolic Logic 3 (4):521-567.

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