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  1. Ontological Tools for Geographic Representation.Roberto Casati, Barry Smith & Achille C. Varzi - 1998 - In Nicola Guarino (ed.), Formal Ontology in Information Systems (FOIS). Ios Press. pp. 77--85.
    This paper is concerned with certain ontological issues in the foundations of geographic representation. It sets out what these basic issues are, describes the tools needed to deal with them, and draws some implications for a general theory of spatial representation. Our approach has ramifications in the domains of mereology, topology, and the theory of location, and the question of the interaction of these three domains within a unified spatial representation theory is addressed. In the final part we also consider (...)
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  • Spatial Reasoning and Ontology: Parts, Wholes, and Locations.Achille C. Varzi - 2007 - In Marco Aiello, Ian E. Pratt-Hartmann & Johan van Benthem (eds.), Handbook of Spatial Logics. Springer Verlag. pp. 945-1038.
    A critical survey of the fundamental philosophical issues in the logic and formal ontology of space, with special emphasis on the interplay between mereology (the theory of parthood relations), topology (broadly understood as a theory of qualitative spatial relations such as continuity and contiguity), and the theory of spatial location proper.
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  • Basic Problems of Mereotopology.Achille C. Varzi - 1998 - In Nicola Guarino (ed.), Formal Ontology in Information Systems. Ios Press. pp. 29–38.
    Mereotopology is today regarded as a major tool for ontological analysis, and for many good reasons. There are, however, a number of open questions that call for an answer. Some are philosophical, others have direct applicative import, but all are crucial for a proper assessment of the strengths and limits of mereotopology. This paper is an attempt to put sum order in this area.
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  • Boundaries, Continuity, and Contact.Achille C. Varzi - 1997 - Noûs 31 (1):26-58.
    There are conflicting intuitions concerning the status of a boundary separating two adjacent entities (or two parts of the same entity). The boundary cannot belong to both things, for adjacency excludes overlap; and it cannot belong to neither, for nothing lies between two adjacent things. Yet how can the dilemma be avoided without assigning the boundary to one thing or the other at random? Some philosophers regard this as a reductio of the very notion of a boundary, which should accordingly (...)
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  • Fiat and Bona Fide Boundaries.Barry Smith & Achille C. Varzi - 2000 - Philosophy and Phenomenological Research 60 (2):401-420.
    There is a basic distinction, in the realm of spatial boundaries, between bona fide boundaries on the one hand, and fiat boundaries on the other. The former are just the physical boundaries of old. The latter are exemplified especially by boundaries induced through human demarcation, for example in the geographic domain. The classical problems connected with the notions of adjacency, contact, separation and division can be resolved in an intuitive way by recognizing this two-sorted ontology of boundaries. Bona fide boundaries (...)
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  • A Complete Axiom System for Polygonal Mereotopology of the Real Plane.Ian Pratt & Dominik Schoop - 1998 - 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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  • Complementation in Representable Theories of Region-Based Space.Torsten Hahmann & Michael Grüninger - 2013 - Notre Dame Journal of Formal Logic 54 (2):177-214.
    Through contact algebras we study theories of mereotopology in a uniform way that clearly separates mereological from topological concepts. We identify and axiomatize an important subclass of closure mereotopologies called unique closure mereotopologies whose models always have orthocomplemented contact algebras , an algebraic counterpart. The notion of MT-representability, a weak form of spatial representability but stronger than topological representability, suffices to prove that spatially representable complete OCAs are pseudocomplemented and satisfy the Stone identity. Within the resulting class of contact algebras (...)
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  • 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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  • Indeterminate Propositions in Prior Analytics I.41.Marko Malink - 2009 - History of Philosophy & Logical Analysis 12 (1):165-189.
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  • I trabocchetti della rappresentazione spaziale.Roberto Casati & Achille C. Varzi - 1999 - Sistemi Intelligent 11 (1):7–28.
    This is a position article summarizing our approach to the philosophy of space and spatial representation. Our concern is mostly methodological: above all, we argue that a number of philosophical puzzles that arise in this field—puzzles concerning the nature of spatial entities, their material and mereological constitution, their relationship with the space that they occupy—stem from a confusion between semantic issues and true metaphysical concerns.
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  • Mereotopological Connection.Anthony G. Cohn & Achille C. Varzi - 2003 - Journal of Philosophical Logic 32 (4):357-390.
    The paper outlines a model-theoretic framework for investigating and comparing a variety of mereotopological theories. In the first part we consider different ways of characterizing a mereotopology with respect to (i) the intended interpretation of the connection primitive, and (ii) the composition of the admissible domains of quantification (e.g., whether or not they include boundary elements). The second part extends this study by considering two further dimensions along which different patterns of topological connection can be classified - the strength of (...)
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  • Expressivity in Polygonal, Plane Mereotopology.Ian Pratt & Dominik Schoop - 2000 - 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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