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  1. Heyting Mereology as a Framework for Spatial Reasoning.Thomas Mormann - 2013 - Axiomathes 23 (1):137- 164.
    In this paper it is shown that Heyting and Co-Heyting mereological systems provide a convenient conceptual framework for spatial reasoning, in which spatial concepts such as connectedness, interior parts, (exterior) contact, and boundary can be defined in a natural and intuitively appealing way. This fact refutes the wide-spread contention that mereology cannot deal with the more advanced aspects of spatial reasoning and therefore has to be enhanced by further non-mereological concepts to overcome its congenital limitations. The allegedly unmereological concept of (...)
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  • A New Universal Bundle Theory.Ruoyu Zhang - 2018 - Philosophia 46 (2):473-486.
    Universal Bundle Theory holds that objects are fundamentally identical with bundles of universals. Universals are multiply instantiable properties. One popular objection to UBT concerns the possibility of distinct indiscernibles. There are mainly two replies in the literature, corresponding to two representative UBTs, which I shall call the Identity-View and the Instance-View. Each view faces serious problems. This paper proposes a new version of UBT and argues that it is better than these other two versions.
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  • Vague Size Predicates.Thomas Bittner - 2011 - Applied Ontology 6 (4):317-343.
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  • Logical Properties of Foundational Mereogeometrical Relations in Bio-Ontologies.Thomas Bittner - 2009 - Applied Ontology 4 (2):109-138.
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  • The Structure of Gunk: Adventures in the Ontology of Space.Jeffrey Sanford Russell - 2008 - In Dean Zimmerman (ed.), Oxford Studies in Metaphysics: Volume 4. Oxford University Press. pp. 248.
    Could space consist entirely of extended regions, without any regions shaped like points, lines, or surfaces? Peter Forrest and Frank Arntzenius have independently raised a paradox of size for space like this, drawing on a construction of Cantor’s. I present a new version of this argument and explore possible lines of response.
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  • 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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  • The Chimeric Self: A Neo Naturalist Bundle Theory of the Self.Lucrezia Compiani - 2019 - Frontiers in Psychology 10.
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  • A Constructivist Perspective on Physics.Peter Fletcher - 2002 - Philosophia Mathematica 10 (1):26-42.
    This paper examines the problem of extending the programme of mathematical constructivism to applied mathematics. I am not concerned with the question of whether conventional mathematical physics makes essential use of the principle of excluded middle, but rather with the more fundamental question of whether the concept of physical infinity is constructively intelligible. I consider two kinds of physical infinity: a countably infinite constellation of stars and the infinitely divisible space-time continuum. I argue (contrary to Hellman) that these do not. (...)
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  • A Plea for Complex Categories in Ontologies.Alexandra Arapinis & Laure Vieu - 2015 - Applied Ontology 10 (3-4):285-296.
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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 Spatio-Temporal Ontology for Geographic Information Integration.Thomas Bittner & Barry Smith - 2009 - International Journal for Geographical Information Science 23 (6):765-798.
    This paper presents an axiomatic formalization of a theory of top-level relations between three categories of entities: individuals, universals, and collections. We deal with a variety of relations between entities in these categories, including the sub-universal relation among universals and the parthood relation among individuals, as well as cross-categorial relations such as instantiation and membership. We show that an adequate understanding of the formal properties of such relations – in particular their behavior with respect to time – is critical for (...)
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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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  • Perché i buchi sono importanti. Problemi di rappresentazione spaziale.Roberto Casati & Achille C. Varzi - 1997 - Sapere 63 (2):38–43.
    The methodological anarchy that characterizes much recent research in artificial intelligence and other cognitive sciences has brought into existence (sometimes resumed) a large variety of entities from a correspondingly large variety of (sometimes dubious) ontological categories. Recent work in spatial representation and reasoning is particularly indicative of this trend. Our aim in this paper is to suggest some ways of reconciling such a luxurious proliferation of entities with the sheer sobriety of good philosophy.
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  • The Niche.Barry Smith & Achille C. Varzi - 1999 - Noûs 33 (2):214-238.
    The concept of niche (setting, context, habitat, environment) has been little studied by ontologists, in spite of its wide application in a variety of disciplines from evolutionary biology to economics. What follows is a first formal theory of this concept, a theory of the relations between objects and their niches. The theory builds upon existing work on mereology, topology, and the theory of spatial location as tools of formal ontology. It will be illustrated above all by means of simple biological (...)
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  • Gestalt Models for Data Decomposition and Functional Architecture in Visual Neuroscience.Carmelo Calì - 2013 - Gestalt Theory 35 (3).
    Attempts to introduce Gestalt theory into the realm of visual neuroscience are discussed on both theoretical and experimental grounds. To define the framework in which these proposals can be defended, this paper outlines the characteristics of a standard model, which qualifies as a received view in the visual neurosciences, and of the research into natural images statistics. The objections to the standard model and the main questions of the natural images research are presented. On these grounds, this paper defends the (...)
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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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  • 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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  • Mereology.Achille C. Varzi - 2016 - Stanford Encyclopedia of Philosophy.
    An overview of contemporary part-whole theories, with reference to both their axiomatic developments and their philosophical underpinnings.
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  • Basic Concepts of Formal Ontology.Barry Smith - 1998 - In Nicola Guarino (ed.), Formal Ontology in Information Systems. IOS Press. pp. 19-28.
    The term ‘formal ontology’ was first used by the philosopher Edmund Husserl in his Logical Investigations to signify the study of those formal structures and relations – above all relations of part and whole – which are exemplified in the subject-matters of the different material sciences. We follow Husserl in presenting the basic concepts of formal ontology as falling into three groups: the theory of part and whole, the theory of dependence, and the theory of boundary, continuity and contact. These (...)
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  • A Proof System for Contact Relation Algebras.Ivo Düntsch & Ewa Orłowska - 2000 - Journal of Philosophical Logic 29 (3):241-262.
    Contact relations have been studied in the context of qualitative geometry and physics since the early 1920s, and have recently received attention in qualitative spatial reasoning. In this paper, we present a sound and complete proof system in the style of Rasiowa and Sikorski (1963) for relation algebras generated by a contact relation.
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  • Ontological Categories in GOL.Barbara Heller & Heinrich Herre - 2004 - Axiomathes 14 (1-3):57-76.
    General Ontological Language (GOL) is a formal framework for representing and building ontologies. The purpose of GOL is to provide a system of top-level ontologies which can be used as a basis for building domain-specific ontologies. The present paper gives an overview about the basic categories of the GOL-ontology. GOL is part of the work of the research group Ontologies in Medicine (Onto-Med) at the University of Leipzig which is based on the collaborative work of the Institute of Medical Informatics (...)
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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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  • Mereological Commitments.Achille C. Varzi - 2000 - Dialectica 54 (4):283–305.
    We tend to talk about (refer to, quantify over) parts in the same way in which we talk about whole objects. Yet a part is not something to be included in an inventory of the world over and above the whole to which it belongs, and a whole is not something to be included in the inventory over and above its constituent parts. This paper is an attempt to clarify a way of dealing with this tension which may be labeled (...)
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  • Lexical Inheritance with Meronymic Relationships.Pablo Gamallo - 2013 - Axiomathes 23 (1):165-185.
    In most computational ontologies, information inheritance is based on the taxonomic relation is_a. A given type inherits from other type only if the latter subsumes the former. We assume, however, that inheritance can be related, not only to the taxonomic relation, but also to the meronymic relationship between parts and wholes. The main aim of this paper is to organise upper-level ontologies associated with lexical information by taking into account part-whole subsumption. As we consider that parts may subsume wholes under (...)
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  • No Time, No Wholes: A Temporal and Causal-Oriented Approach to the Ontology of Wholes. [REVIEW]Riccardo Manzotti - 2009 - Axiomathes 19 (2):193-214.
    What distinguishes a whole from an arbitrary sum of elements? I suggest a temporal and causal oriented approach. I defend two connected claims. The former is that existence is, by every means, coextensive with being the cause of a causal process. The latter is that a whole is the cause of a causal process with a joint effect. Thus, a whole is something that takes place in time. The approach endorses an unambiguous version of Restricted Composition that suits most commonsensical (...)
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  • 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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  • Formal Ontology of Space, Time, and Physical Entities in Classical Mechanics.Thomas Bittner - 2018 - Applied Ontology 13 (2):135-179.
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  • Reasoning About Space: The Hole Story.Achille C. Varzi - 1996 - Logic and Logical Philosophy 4:3-39.
    This is a revised and extended version of the formal theory of holes outlined in the Appendix to the book "Holes and Other Superficialities". The first part summarizes the basic framework (ontology, mereology, topology, morphology). The second part emphasizes its relevance to spatial reasoning and to the semantics of spatial prepositions in natural language. In particular, I discuss the semantics of ‘in’ and provide an account of such fallacious arguments as “There is a hole in the sheet. The sheet is (...)
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  • Nisza.Achille C. Varzi & Barry Smith - 2000 - Filozofia Nauki 3:5–30.
    The concept of niche (setting, context, habitat, environment) has been little studied by ontologists, in spite of its wide application in a variety of disciplines from evolutionary biology to economics. What follows is a first formal theory of this concept, a theory of the relations between objects and their niches. The theory builds upon existing work on mereology, topology, and the theory of spatial location as tools of formal ontology. It is illustrated above all by means of simple biological examples, (...)
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  • The Many Facets of Identity Criteria.Pierdaniele Giaretta Massimiliano Carrara - 2004 - Dialectica 58 (2):221-232.
    The aim of this note is to discuss the general form and role of identity criteria. We have taken two readings into consideration which express two different functions of identity criteria. The first expresses the epistemic function whilst the second deals with the ontological function. We argue that there are several problems related to the specification of both these functions. As a consequence, we conclude that identity criteria are not necessary to provide ontological legitimacy.
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  • The Many Facets of Identity Criteria.Massimiliano Carrara & Pierdaniele Giaretta - 2004 - Dialectica 58 (2):221–232.
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  • Modal Logics Based on Mathematical Morphology for Qualitative Spatial Reasoning.Isabelle Bloch - 2002 - Journal of Applied Non-Classical Logics 12 (3-4):399-423.
    We propose in this paper to construct modal logics based on mathematical morphology. The contribution of this paper is twofold. First we show that mathematical morphology can be used to define modal operators in the context of normal modal logics. We propose definitions of modal operators as algebraic dilations and erosions, based on the notion of adjunction. We detail the particular case of morphological dilations and erosions, and of there compositions, as opening and closing. An extension to the fuzzy case (...)
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  • The Naive Topology of the Conscious Subject.Rory Madden - 2015 - Noûs 49 (1):55-70.
    What does our naïve conception of a conscious subject demand of the nature of conscious beings? In a series of recent papers David Barnett has argued that a range of powerful intuitions in the philosophy of mind are best explained by the hypothesis that our naïve conception imposes a requirement of mereological simplicity on the nature of conscious beings. It is argued here that there is a much more plausible explanation of the intuitions in question. Our naïve conception of a (...)
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  • Mereological Commitments.Achille C. Varzi - 2000 - Dialectica 54 (4):283-305.
    We tend to talk about parts in the same way in which we talk about whole objects. Yet a part is not something to be included in an inventory of the world over and above the whole to which it belongs, and a whole is not something to be included in an inventory over and above its own parts. This paper is an attempt to clarify a way of dealing with this tension which may be labeled the Minimalist View: an (...)
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