Results for 'mereotopology'

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  1. Quantum Mereotopology.Barry Smith & Berit O. Brogaard - 2002 - Annals of Mathematics and Artificial Intelligence 36 (1):153-175.
    Mereotopology faces problems when its methods are extended to deal with time and change. We offer a new solution to these problems, based on a theory of partitions of reality which allows us to simulate (and also to generalize) aspects of set theory within a mereotopological framework. This theory is extended to a theory of coarse- and fine-grained histories (or finite sequences of partitions evolving over time), drawing on machinery developed within the framework of the so-called ‘consistent histories’ interpretation (...)
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  2. Mereotopology: A Theory of Parts and Boundaries.Barry Smith - 1996 - Data and Knowledge Engineering 20 (3):287–303.
    The paper is a contribution to formal ontology. It seeks to use topological means in order to derive ontological laws pertaining to the boundaries and interiors of wholes, to relations of contact and connectedness, to the concepts of surface, point, neighbourhood, and so on. The basis of the theory is mereology, the formal theory of part and whole, a theory which is shown to have a number of advantages, for ontological purposes, over standard treatments of topology in set-theoretic terms. One (...)
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  3.  22
    A Mereotopology Based on Sequent Algebras.Dimiter Vakarelov - 2017 - Journal of Applied Non-Classical Logics 27 (3-4):342-364.
    Mereotopology is an extension of mereology with some relations of topological nature like contact. An algebraic counterpart of mereotopology is the notion of contact algebra which is a Boolean algebra whose elements are considered to denote spatial regions, extended with a binary relation of contact between regions. Although the language of contact algebra is quite expressive to define many useful mereological relations and mereotopological relations, there are, however, some interesting mereotopological relations which are not definable in it. Such (...)
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  4. Mereotopology without Mereology.Peter Forrest - 2010 - Journal of Philosophical Logic 39 (3):229-254.
    Mereotopology is that branch of the theory of regions concerned with topological properties such as connectedness. It is usually developed by considering the parthood relation that characterizes the, perhaps non-classical, mereology of Space (or Spacetime, or a substance filling Space or Spacetime) and then considering an extra primitive relation. My preferred choice of mereotopological primitive is interior parthood . This choice will have the advantage that filters may be defined with respect to it, constructing “points”, as Peter Roeper has (...)
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  5. 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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  6. Boundaries: An Essay in Mereotopology.Barry Smith - 1997 - In Lewis H. Hahn (ed.), Philosophy of Roderick Chisholm (Library of Living Philosophers). Open Court. pp. 534--561.
    Of Chisholm’s many signal contributions to analytic metaphysics, perhaps the most important is his treatment of boundaries, a category of entity that has been neglected, to say the least, in the history of ontology. We can gain some preliminary idea of the sorts of problems which the Chisholmian ontology of boundaries is designed to solve, if we consider the following Zeno-inspired thought-experiment.
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  7. Parts, Wholes, and Part-Whole Relations: The Prospects of Mereotopology.Achille C. Varzi - 1996 - Data and Knowledge Engineering 20:259–286.
    We can see mereology as a theory of parthood and topology as a theory of wholeness. How can these be combined to obtain a unified theory of parts and wholes? This paper examines various non-equivalent ways of pursuing this task, with specific reference to its relevance to spatio-temporal reasoning. In particular, three main strategies are compared: (i) mereology and topology as two independent (though mutually related) chapters; (ii) mereology as a general theory subsuming topology; (iii) topology as a general theory (...)
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  8.  63
    Elementary Polyhedral Mereotopology.Ian Pratt-Hartmann & Dominik Schoop - 2002 - 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, (...)
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  9.  28
    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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  10.  24
    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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  11.  40
    The Mereotopology of Time.Claudio Mazzola - 2019 - Notre Dame Journal of Formal Logic 60 (2):215-252.
    Mereotopology is the discipline obtained from combining topology with the formal study of parts and their relation to wholes, or mereology. This article develops a mereotopological theory of time, illustrating how different temporal topologies can be effectively discriminated on this basis. Specifically, we demonstrate how the three principal types of temporal models—namely, the linear ones, the forking ones, and the circular ones—can be characterized by differently combining two sole mereotopological constraints: one to denote the absence of closed loops, and (...)
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  12.  6
    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 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 two (...)
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  13. A Modal Approach to Dynamic Ontology: Modal Mereotopology.Dimiter Vakarelov - 2008 - Logic and Logical Philosophy 17 (1-2):163-183.
    In this paper we show how modal logic can be applied in the axiomatizations of some dynamic ontologies. As an example we consider the case of mereotopology, which is an extension of mereology with some relations of topological nature like contact relation. We show that in the modal extension of mereotopology we may define some new mereological and mereotopological relations with dynamic nature like stable part-of and stable contact. In some sense such “stable” relations can be considered as (...)
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  14.  11
    Mereotopology in 2nd-Order and Modal Extensions of Intuitionistic Propositional Logic.Paolo Torrini, John G. Stell & Brandon Bennett - 2002 - Journal of Applied Non-Classical Logics 12 (3-4):495-525.
    We show how mereotopological notions can be expressed by extending intuitionistic propositional logic with propositional quantification and a strong modal operator. We first prove completeness for the logics wrt Kripke models; then we trace the correspondence between Kripke models and topological spaces that have been enhanced with an explicit notion of expressible region. We show how some qualitative spatial notions can be expressed in topological terms. We use the semantical and topological results in order to show how in some extensions (...)
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  15.  85
    A Necessary Relation Algebra for Mereotopology.Ivo DÜntsch, Gunther Schmidt & Michael Winter - 2001 - Studia Logica 69 (3):381 - 409.
    The standard model for mereotopological structures are Boolean subalgebras of the complete Boolean algebra of regular closed subsets of a nonempty connected regular T 0 topological space with an additional "contact relation" C defined by xCy x ØA (possibly) more general class of models is provided by the Region Connection Calculus (RCC) of Randell et al. We show that the basic operations of the relational calculus on a "contact relation" generate at least 25 relations in any model of the RCC, (...)
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  16.  13
    Dynamic Relational Mereotopology.Vladislav Nenchev - 2013 - Logic and Logical Philosophy 22 (3):295-325.
    In this paper we present stable and unstable versions of several well-known relations from mereotopology: part-of, overlap, underlap and contact. An intuitive semantics is given for the stable and unstable relations, describing them as dynamic counterparts of the base mereotopo-logical relations. Stable relations are described as ones that always hold, while unstable relations hold sometimes. A set of first-order sentences is provided to serve as axioms for the stable and unstable relations, and representation theory is developed in similar fashion (...)
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  17.  18
    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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  18.  24
    A Necessary Relation Algebra for Mereotopology.D.[Uuml ]Ntsch Ivo, Schmidt Gunther & Winter Michael - 2001 - Studia Logica 69 (3):381-409.
    The standard model for mereotopological structures are Boolean subalgebras of the complete Boolean algebra of regular closed subsets of a nonempty connected regular T0 topological space with an additional "contact relation" C defined by xCy ? x n ? Ø.
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  19.  41
    Mendelssohn, Kant, and the Mereotopology of Immortality.Jonathan Simon & Colin Marshall - 2017 - Ergo: An Open Access Journal of Philosophy 4.
    In the first Critique, Kant claims to refute Moses Mendelssohn’s argument for the immortality of the soul. But some commentators, following Bennett (1974), have identified an apparent problem in the exchange: Mendelssohn appears to have overlooked the possibility that the “leap” between existence and non-existence might be a boundary or limit point in a continuous series, and Kant appears not to have exploited the lacuna, but to have instead offered an irrelevant criticism. Here, we argue that even if these commentators (...)
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  20.  98
    Consistent Quantum Mechanics Admits No Mereotopology.Chris Fields - 2012 - Axiomathes (1):1-10.
    It is standardly assumed in discussions of quantum theory that physical systems can be regarded as having well-defined Hilbert spaces. It is shown here that a Hilbert space can be consistently partitioned only if its components are assumed not to interact. The assumption that physical systems have well-defined Hilbert spaces is, therefore, physically unwarranted.
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  21.  6
    Consistent Quantum Mechanics Admits No Mereotopology.Chris Fields - 2014 - Axiomathes 24 (1):9-18.
    It is standardly assumed in discussions of quantum theory that physical systems can be regarded as having well-defined Hilbert spaces. It is shown here that a Hilbert space can be consistently partitioned only if its components are assumed not to interact. The assumption that physical systems have well-defined Hilbert spaces is, therefore, physically unwarranted.
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  22.  13
    Dynamic Relational Mereotopology: Logics for Stable and Unstable Relations.Vladislav Nenchev - 2013 - Logic and Logical Philosophy 22 (3):295-325.
    In this paper we present stable and unstable versions of several well-known relations from mereotopology: part-of, overlap, underlap and contact. An intuitive semantics is given for the stable and unstable relations, describing them as dynamic counterparts of the base mereotopo-logical relations. Stable relations are described as ones that always hold, while unstable relations hold sometimes. A set of first-order sentences is provided to serve as axioms for the stable and unstable relations, and representation theory is developed in similar fashion (...)
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  23.  23
    Whitehead's Mereotopology and the Project of Formal Ontology.Sébastien Richard - 2011 - Logique Et Analyse 54 (216).
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  24. Adding Convexity to Mereotopology.Marion Haemmerli & Achille C. Varzi - 2014 - In Pawel Garbacz & Oliver Kutz (eds.), Formal Ontology in Information Systems. Proceedings of the Eighth International Conference. IOS Press. pp. 65–78.
    Convexity predicates and the convex hull operator continue to play an important role in theories of spatial representation and reasoning, yet their first-order axiomatization is still a matter of controversy. In this paper, we present a new approach to adding convexity to mereotopological theory with boundary elements by specifying first-order axioms for a binary segment operator s. We show that our axioms yields a convex hull operator h that supports, not only the basic properties of convex regions, but also complex (...)
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  25. Why is It No Longer Possible to Build a Formal Ontology as a Mereotopology?Martina Properzi - 2019 - In The Philosophy of Aristotle. Atene, Grecia:
    This brief paper aims to underline which are the philosophical limits of mereotopology, when one takes it as a basic unitary theoretical framework for formal ontology. Mereotopology is a first-order theory of the relations among wholes, parts and the boundaries between parts, that combines mereological and topological concepts. Nowadays, with the expression “formal ontology” one intends either the computational (engineering) version, or the philosophical (categorial) one. It is important, then, to avoid terminological confusions. The main philosophical reason that (...)
     
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  26.  9
    CODI: A Multidimensional Theory of Mereotopology with Closure Operations.Torsten Hahmann - 2020 - Applied Ontology 15 (3):251-311.
    No categories
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  27. 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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  28.  28
    On the Decidability of Axiomatized Mereotopological Theories.Hsing-Chien Tsai - 2015 - Notre Dame Journal of Formal Logic 56 (2):287-306.
    The signature of the formal language of mereotopology contains two predicates $P$ and $C$, which stand for “being a part of” and “contact,” respectively. This paper will deal with the decidability issue of the mereotopological theories which can be formed by the axioms found in the literature. Three main results to be given are as follows: all axiomatized mereotopological theories are separable; all mereotopological theories up to $\mathbf{ACEMT}$, $\mathbf{SACEMT}$, or $\mathbf{SACEMT}^{\prime}$ are finitely inseparable; all axiomatized mereotopological theories except $\mathbf{SAX}$, (...)
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  29. Layers: A New Approach to Locating Objects in Space.Maureen Donnelly & Barry Smith - 2003 - In W. Kuhn M. F. Worboys & S. Timpf (eds.), Spatial Information Theory: Foundations of Geographic Informa­tion Science. Springer. pp. 50-65.
    Standard theories in mereotopology focus on relations of parthood and connection among spatial or spatio-temporal regions. Objects or processes which might be located in such regions are not normally directly treated in such theories. At best, they are simulated via appeal to distributions of attributes across the regions occupied or by functions from times to regions. The present paper offers a richer framework, in which it is possible to represent directly the relations between entities of various types at different (...)
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  30. 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 (...)
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  31. Metaphysics.Barry Smith - 2010 - In Asbjørn Steglich-Petersen (ed.), Metaphysics: Five Questions. Automatic Press. pp. 143-158.
    Attempts to trace a unifying thread of ontological realism extending through 1. my early writings on Frege, Brentano, Husserl, Wittgenstein, Ingarden and (with Kevin Mulligan and Peter Simons) on truthmakers; 2. work on formal theories of the common-sense world, and on mereotopology, fiat objects, geographical categories, and environments (with David Mark, Roberto Casati, Achille Varzi), to 3. current work on applied ontology in biology and medicine, and on the theory of document acts and on the ontology of information artifacts.
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  32.  77
    Inconsistent Boundaries.Zach Weber & A. J. Cotnoir - 2015 - Synthese 192 (5):1267-1294.
    Mereotopology is a theory of connected parts. The existence of boundaries, as parts of everyday objects, is basic to any such theory; but in classical mereotopology, there is a problem: if boundaries exist, then either distinct entities cannot be in contact, or else space is not topologically connected . In this paper we urge that this problem can be met with a paraconsistent mereotopology, and sketch the details of one such approach. The resulting theory focuses attention on (...)
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  33.  16
    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 (...)
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  34. Ontology and the Logistic Analysis of Reality.Barry Smith - 1993 - In Nicola Guarino & Roberto Poli (eds.), Proceedings of the International Workshop on Formal Ontology in Conceptual Analysis and Knowledge Representation. Italian National Research Council. pp. 51-68.
    I shall attempt in what follows to show how mereology, taken together with certain topological notions, can yield the basis for future investigations in formal ontology. I shall attempt to show also how the mereological framework here advanced can allow the direct and natural formulation of a series of theses – for example pertaining to the concept of boundary – which can be formulated only indirectly (if at all) in set-theoretic terms.
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  35. Kognitionsforskningens topologiske grundlag.Barry Smith - 2003 - Semikolon 3 (7):91-105.
    The paper introduces the concepts at the heart of point-set-topology and of mereotopology (topology founded in the non-atomistic theory of parts and wholes) in an informal and intuitive fashion. It will then seek to demonstrate how mereotopological ideas can be of particular utility in cognitive science applications. The prehistory of such applications (in the work of Husserl, the Gestaltists, of Kurt Lewin and of J. J. Gibson) will be sketched, together with an indication of the field of possibilities in (...)
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  36.  23
    Finitely Inseparable First-Order Axiomatized Mereotopological Theories.Hsing-Chien Tsai - 2013 - Logic and Logical Philosophy 22 (3):347-363.
    This paper will first introduce first-order mereotopological axioms and axiomatized theories which can be found in some recent literature and it will also give a survey of decidability, undecidability as well as other relevant notions. Then the main result to be given in this paper will be the finite inseparability of any mereotopological theory up to atomic general mereotopology (AGEMT) or strong atomic general mereotopology (SAGEMT). Besides, a more comprehensive summary will also be given via making observations about (...)
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  37. 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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  38. 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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  39.  99
    Boundary.Achille C. Varzi - 2013 - Stanford Encyclopedia of Philosophy.
    We think of a boundary whenever we think of an entity demarcated from its surroundings. There is a boundary (a line) separating Maryland and Pennsylvania. There is a boundary (a circle) isolating the interior of a disc from its exterior. There is a boundary (a surface) enclosing the bulk of this apple. Sometimes the exact location of a boundary is unclear or otherwise controversial (as when you try to trace out the margins of Mount Everest, or even the boundary of (...)
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  40. Zur Kognition räumlicher Grenzen: Eine mereotopologische Untersuchung.Barry Smith - 1995 - Kognitionswissenschaft 4:177-184.
    The perception of spatial bodies is at least in part a perception of bodily boundaries or surfaces. The usual mathematical conception of boundaries as abstract constructions is, however, of little use for cognitive science purposes. The essay therefore seeks a more adequate conception of the ontology of boundaries building on ideas in Aristotle and Brentano on what we may call the coincidence of boundaries. It presents a formal theory of boundaries and of the continua to which they belong, of a (...)
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  41.  79
    The Formal Structure of Ecological Contexts.Barry Smith & Achille C. Varzi - 1999 - In Paolo Bouquet, Patrick Brezillon, Francesca Castellani & Luciano Serafini (eds.), Modeling and Using Context. Proceedings of the Second International and Interdisciplinary Conference. Springer. pp. 339–350.
    This is an informal presentation of the theory of niches understood as ecological contexts. The first part sets out the basic conceptual background. The second part outlines the main principles of the theory and addresses the question of how the theory can be extended to aid our thinking in relation to the special types of causal integrity that characterize niches and niched entities.
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  42. Truth and the Visual Field.Barry Smith - 1999 - In Jean Petitot, F. J. Varela, Bernard Pachoud & J.-M. Roy (eds.), Naturalizing Phenomenology: Issues in Contemporary Phenomenology and Cognitive Science. Stanford: Stanford University Press. pp. 317-329.
    The paper uses the tools of mereotopology (the theory of parts, wholes and boundaries) to work out the implications of certain analogies between the 'ecological psychology' of J. J Gibson and the phenomenology of Edmund Husserl. It presents an ontological theory of spatial boundaries and of spatially extended entities. By reference to examples from the geographical sphere it is shown that both boundaries and extended entities fall into two broad categories: those which exist independently of our cognitive acts (for (...)
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  43. Boundaries: A Brentanian Theory.Barry Smith - 2000 - Brentano Studien 8:107-114.
    According to Brentano's theory of boundaries, no boundary can exist without being connected with a continuum. But there is no specifiable part of the continuum, and no point, which is such that we may say that it is the existence of that part or of that point which conditions the boundary. - An adequate theory of the continuum must now recognize that boundaries be boundaries only in certain directions and not in others. This leads to consequences in other areas, too.
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  44.  86
    The Formal Ontology of Boundaries.Barry Smith & Achille C. Varzi - 1997 - Electronic Journal of Analytic Philosophy 5 (5).
    Revised version published as Barry Smith and Achille Varzi, “Fiat and Bona Fide Boundaries”, Philosophy and Phenomenological Research, 60: 2 (March 2000), 401–420.
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  45.  91
    La verità e il campo visivo.Barry Smith - 1999 - Paradigmi 17:49-62.
    L'articolo usa la teoria delle parti, del tutto e dei contomi per elaborare alcune relazioni cruciali tra la «psicologia ecologica» di J.J. Gibson e la fenomenologia di Husserl. Presenta, inoltre, una teoria ontologica dei contomi spaziali e delle entita spazialmente estese, applicandola al cam po visivo, qui concepito come un' entita spazialmente estesa dipendente dal soggetto che percepisce. Su questa base e possibile formulare un nuovo tipo di definizione teoretico-correspondentista della verita per gli enunciati del linguaggio naturale.
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  46.  45
    Oggetti fiat.Barry Smith - 2002 - Rivista di Estetica 42 (2):58–87.
    Extended entities have boundaries of two different sorts: those that do, and those that do not correspond to physical discontinuities. Call the first sort (coastlines, the surface of your nose) bona fide boundaries; and the second (the boundary of Montana, the boundary separating your upper from your lower torso) fiat boundaries. Fiat boundaries are found especially in the geographic realm, but are involved wherever language carves out portions of reality in ways which do not reflect physical discontinuities. These ideas are (...)
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  47. Topological Essentialism.Roberto Casati & Achille C. Varzi - 2000 - Philosophical Studies 100 (3):217-236.
    Considering topology as an extension of mereology, this paper analyses topological variants of mereological essentialism (the thesis that an object could not have different parts than the ones it has). In particular, we examine de dicto and de re versions of two theses: (i) that an object cannot change its external connections (e.g., adjacent objects cannot be separated), and (ii) that an object cannot change its topological genus (e.g., a doughnut cannot turn into a sphere). Stronger forms of structural essentialism, (...)
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  48. Fiat and Bona Fide Boundaries: Towards an Ontology of Spatially Extended Objects.Barry Smith & Achille C. Varzi - 1997 - In Stephen Hirtle & Andrew U. Frank (eds.), Spatial Information Theory: International Conference COSIT ‘97. Springer. pp. 103–119.
    Human cognitive acts are directed towards objects extended in space of a wide range of different types. What follows is a new proposal for bringing order into this typological clutter. The theory of spatially extended objects should make room not only for the objects of physics but also for objects at higher levels, including the objects of geography and of related disciplines. It should leave room for different types of boundaries, including both the bona fide boundaries which we find in (...)
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  49. 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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  50. Topological Foundations of Cognitive Science.Carola Eschenbach, Christopher Habel & Barry Smith (eds.) - 1984 - Hamburg: Graduiertenkolleg Kognitionswissenschaft.
    A collection of papers presented at the First International Summer Institute in Cognitive Science, University at Buffalo, July 1994, including the following papers: ** Topological Foundations of Cognitive Science, Barry Smith ** The Bounds of Axiomatisation, Graham White ** Rethinking Boundaries, Wojciech Zelaniec ** Sheaf Mereology and Space Cognition, Jean Petitot ** A Mereotopological Definition of 'Point', Carola Eschenbach ** Discreteness, Finiteness, and the Structure of Topological Spaces, Christopher Habel ** Mass Reference and the Geometry of Solids, Almerindo E. Ojeda (...)
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