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 the connection and its multiplicity. (shrink)

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 (...) of quantum mechanics. (shrink)

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 (...) done (“Region-based topology”, Journal of Philosophical Logic , 26 (1997), 25–309). This paper generalizes Roeper’s result, relying only on mereotopological axioms, not requiring an underlying classical mereology, and not assuming the Axiom of Choice. I call the resulting mathematical system an approximate lattice , because although meets and joins are not assumed they are approximated. Theorems are proven establishing the existence and uniqueness of representations of approximate lattices, in which their members, the regions, are represented by sets of “points” in a topological “space”. (shrink)

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 (...) the other one to denote the absence of branches. (shrink)

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 (...) central goal of the paper is to provide a rigorous formulation of Brentano's thesis to the effect that a boundary can exist as a matter of necessity only as part of a whole of higher dimension which it is the boundary of. It concludes with a brief survey of current applications of mereotopology in areas such as natural-language analysis, geographic information systems, machine vision, naive physics, and database and knowledge engineering. (shrink)

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 (...) are, for instance, the relation of n-ary contact, internal connectedness and some others. To overcome this disadvantage, we introduce a generalisation of contact algebra, replacing the contact with a binary relation between finite sets of regions and a region, satisfying some formal properties of Tarski consequence relation. The obtained system is called sequent algebra, considered as an algebraic counterpart of a new mereotopology. We develop the topological representation theory for sequent algebras showing in this way certain correspondence between point-free and point-based models of space. As a by-product, we show how one logical relation in nature notion, Tarski consequence relation, may have also certain spatial meaning. (shrink)

Consider the following two metaphysical questions about pregnancy: (1) When does a new organism of a certain kind start to exist? (2) What is the mereological and topological relationship between the pregnant organism and with what it is pregnant? Despite assumptions made in the literature, I take these questions to be independent of each other, such that an answer to one does not provide an answer to the other. I argue that the way to connect them is via a maximality (...) principle that prevents one organism being a proper part of another organism of the same kind. That being said, such a maximality principle need not be held, and may not apply in the case of pregnancy. The aims of this paper are thus to distinguish and connect these metaphysical questions, in order to outline a taxonomy of rival mereotopological models of pregnancy that result from the various combinations of their answers. (shrink)

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 (...) of the logics it is possible to express connectedness, non-emptiness and a set of jointly exhaustive, pairwise disjoint, binary relations that play a significant role in qualitative spatial reasoning. (shrink)

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 (...) as this familiar interpretation. This proposal has the merit of transforming a vague, open-ended question about ontologies for practical mereotopological reasoning into a precise question in model theory. We show that (a version of) the familiar interpretation is countable and atomic, and therefore prime. We conclude that useful alternative ontologies of the plane are, if anything, less parsimonious than the one which they are supposed to replace. (shrink)

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.

In his Critique of Pure Reason Immanuel Kant presents four anti- nomies. In his attempt to solve the first of these antinomies he examines and analyzes"thesis" and "antithesis" more thoroughly and employs the terms `part', `whole' and `boundary' in his argumentation for their validity. According to Kant, the whole problem surrounding the antinomy was caused by applying the concept of the world to nature and then using both terms interchangeably. While interesting, this solution is still not that much more than (...) a well thought out idea if it does not also include an adequate formal explication. Since the aforementioned terms all have counterparts in modern mereotopology, a discipline that has seen significant progress in recent times, we will apply these concepts to Kant's analysis in an attempt to evaluate Kant's solution in light of modern analytic philosophy. (shrink)

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 employs a single primitive binary relation C(x, y) (read: "x is in contact with y"). Thus, in this formalism, all topological facts supervene on facts about contact. Because of its potential application to theories of qualitative spatial reasoning, Whitehead's primitive has recently been the subject of scrutiny from within the Artificial Intelligence community. Various results regarding the mereotopology of the Euclidean plane have been obtained, settling such issues as expressive power, axiomatization and the existence of alternative models. The contribution of the present paper is to extend some of these results to the mereotopology of three-dimensional Euclidean space. Specifically, we show that, in a first-order setting where variables range over tame subsets of ℝ³, Whitehead's primitive is maximally expressive for topological relations; and we deduce a corollary constraining the possible region-based models of the space we inhabit. (shrink)

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 (...) to Stone’s representation theory for Boolean algebras and distributive lattices. Then we present some results about the first-order predicate logic of these relations and about its quantifier-free fragment. Completeness theorems for these logics are proved, the full first-order theory is proved to be hereditary undecidable and the satisfiability problem of the quantifier-free fragment is proved to be NP-complete. (shrink)

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 (...) two first-order mereotopological languages, and investigates their expressive power. It turns out that these languages, notwithstanding the simplicity of their primitives, are surprisingly expressive. In particular, it is shown that infinitary versions of these languages are adequate to express (in a sense made precise below) all topological relations over the domain of polygons in the closed plane. (shrink)

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 ‘xis connected’ or ‘xis a part ofy’, and the entities over which their variables range are, accordingly, notpoints, butregions: spatial entities other than regions are admitted, if at all, only as logical constructs of regions. This paper considers two first-order mereotopological languages, and (...) investigates their expressive power. It turns out that these languages, notwithstanding the simplicity of their primitives, are surprisingly expressive. In particular, it is shown that infinitary versions of these languages are adequate to express (in a sense made precise below) all topological relations over the domain of polygons in the closed plane. (shrink)

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 (...) properties concerning region alignment. We also argue that h is stronger than convex hull operators from existing axiomatizations and show how to derive the latter from our axioms for s. (shrink)

In his Critique of Pure Reason Immanuel Kant presents four antinomies. In his attempt to solve the first of these antinomies he examines and analyzes "thesis" and "antithesis" more thoroughly and employs the terms `part', `whole' and `boundary' in his argumentation for their validity. According to Kant, the whole problem surrounding the antinomy was caused by applying the concept of the world to nature and then using both terms interchangeably. While interesting, this solution is still not that much more than (...) a well thought out idea if it does not also include an adequate formal explication. Since the aforementioned terms all have counterparts in modern mereotopology, a discipline that has seen significant progress in recent times, we will apply these concepts to Kant's analysis in an attempt to evaluate Kant's solution in light of modern analytic philosophy. (shrink)

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.

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 (...) to Stone’s representation theory for Boolean algebras and distributive lattices. Then we present some results about the first-order predicate logic of these relations and about its quantifier-free fragment. Completeness theorems for these logics are proved, the full first-order theory is proved to be hereditary undecidable and the satisfiability problem of the quantifier-free fragment is proved to be NP-complete. (shrink)

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.

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 (...) subsuming mereology. Some more speculative strategies and directions for further research are also considered. (shrink)

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 $\mathbf{SAX}$, (...) $\mathbf{SAX}^{\prime}$, or $\mathbf{S\overline{B}X}^{\prime}$, where $\mathbf{X}$ is strictly stronger than $\mathbf{CEMT}$, are undecidable. Then it can also be easily seen that all axiomatized mereotopological theories proved to be undecidable here are neither essentially undecidable nor strongly undecidable but are hereditarily undecidable. Result will be shown by constructing strongly undecidable mereotopological structures based on two-dimensional Euclidean space, and it will be pointed out that the same construction cannot be carried through if the language is not rich enough. (shrink)

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 (...) are correct, an argument against the leap-as-limit possibility is implicit in claims that Mendelssohn accepts. Moreover, Kant’s criticism of Mendelssohn adapts naturally into a response to this argument, though Mendelssohn endorses further claims which enable him to address this Kantian response. To illustrate the philosophical issues in play, we conclude by noting the affinity between the Mendelssohnian argument we develop and several prominent arguments in contemporary metaphysics: David Lewis’s argument from vagueness for unrestricted composition, Ted Sider’s argument from vagueness for perdurantism, and Peter Unger’s argument from the problem of the many for substance dualism. In short, we argue that the philosophical issues involved in the Mendelssohn-Kant exchange are much richer than previous commentators have believed, and that there is a Mendelssohnian argument for the immortality of the soul (or anyway, the permanence of simples) that does not suffer from any obvious flaw. (shrink)

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, (...) and hence, in any standard model of mereotopology. It follows that the expressiveness of the RCC in relational logic is much greater than the original 8 RCC base relations might suggest. We also interpret these 25 relations in the the standard model of the collection of regular open sets in the two-dimensional Euclidean plane. (shrink)

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. (shrink)

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 (...) approximations of the “essential relations” in the domain of mereotopology. (shrink)

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 (...) other properties stronger than undecidability. (shrink)

In the graphical representation of ontologies, it is customary to use graph theory as the representational background. We claim here that the standard graph-based approach has a number of limitations. We focus here on a problem in the graph-based representation of ontologies in complex domains such as biomedical, engineering and manufacturing: lack of mereotopological representation. Based on such limitation, we proposed a diagrammatic way to represent an entity’s structure and various forms of mereotopological relationships between the entities.

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 (...) keeps me from developing the connection between computational and philosophical formal ontologies on mereotopological basis is the following: anti-Representationalism and Monism are two ontological stances very difficult to join together, as mereotopology does, if one takes into account the ontological implications of the emerging dynamical dual paradigm in the information theoretic approach to quantum physics. In general, it is this approach to the current fundamental and experimentally extremely successful physical theories about the microphysical realm, namely Quantum Mechanics and Quantum Field Theory, that allows to overcome the “gap” between the two disciplinary fields of formal ontology, making information a physical magnitude. I do not oppose anti-Representationalism, but its connection with the monistic stance, because of the fact that nowadays information appears as a basic component of the microphysical realm just like energy-matter. This fact justifies a realistic but information-matter dual ontology as the proper formal ontology of the emerging paradigm in the information theoretic approach to contemporary quantum physics. The primacy that Aristotle gives to the theory of principle (act/potency) as to the theory of categories is a very helpful tool to solve the main question that arises within a realistic dual ontological theoretical framework: the question of the non-stable nature of the categories, that reflect the increasingly complexity of the physical dynamic realistic orders. Here is the importance of an historical approach to the topic, given also the fact that mereological formal ontology originates with the works of three authors (Bolzano, Brentano, Husserl) that studied, directly or indirectly, Aristotle’s ontology. (shrink)

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.

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.

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 (...) ** Defining a 'Doughnut' Made Difficult, N .M. Gotts ** A Theory of Spatial Regions with Indeterminate Boundaries, A.G. Cohn and N.M. Gotts ** Mereotopological Construction of Time from Events, Fabio Pianesi and Achille C. Varzi ** Computational Mereology: A Study of Part-of Relations for Multi-media Indexing, Wlodek Zadrozny and Michelle Kim. (shrink)

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 (...) levels, including both objects and the regions they occupy. What results is a layered mereotopology, a theory which can handle multiple layers (analogous to the layers of a lasagna) of spatially or spatiotemporally coincident but mereologically non-overlapping entities. (shrink)

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 (...) yield a notion of contact that is effectively modeled by classical topology; the analogue of contact involving fiat boundaries calls, however, for a different account, based on the intuition that fiat boundaries do not support the open/closed distinction on which classical topology is based. In the presence of this two-sorted ontology it then transpires that mereotopology—topology erected on a mereological basis—is more than a trivial formal variant of classical point-set topology. (shrink)

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 the strength of the algebraic complementation delineates two classes of mereotopology according to the key ontological choice between mereological and topological closure operations. All closure operations are defined mereologically if and only if the corresponding contact algebras are uniquely complemented while topological closure operations highly restrict the contact relation but allow not uniquely complemented and nondistributive contact algebras. Each class contains a single ontologically coherent theory that admits discrete models. (shrink)

Euclid’s definition of a point as “that which has no part” has been a major source of controversy in relation to the epistemological and ontological presuppositions of classical geometry, from the medieval and modern disputes on indivisibilism to the full development of point-free geometries in the 20th century. Such theories stem from the general idea that all talk of points as putative lower-dimensional entities must and can be recovered in terms of suitable higher-order constructs involving only extended regions (or bodies). (...) Here I focus on what is arguably the first thorough proposal of this sort, Whitehead’s theory of “extensive abstraction”, offering a critical reconstruction of the theory through its successive installments: from the purely mereological version of ‘La théorie relationniste de l’espace’ (1916) to the refined versions presented in An Enquiry Concerning the Principles of Natural Knowledge (1919) and in The Concept of Nature (1920) to the last, mereotopological version of Process and Reality (1929). (shrink)

If two self-connected individuals are connected, it follows in classical extensional mereotopology that the sum of those individuals is self-connected too. Since mainland Europe and mainland Asia, for example, are both self-connected and connected to each other, mainland Eurasia is also self-connected. In contrast, in non-extensional mereotopologies, two individuals may have more than one sum, in which case it does not follow from their being self-connected and connected that the sum of those individuals is self-connected too. Nevertheless, one would (...) still expect it to follow that a sum of connected self-connected individuals is self-connected too. In this paper, we present some surprising countermodels which show that this conjecture is incorrect. (shrink)

In fields such as medicine, geography, and mechanics, spatial reasoning involves reasoning about entities that may coincide without overlapping. Some examples are: cavities and invading particles, passageways and valves, geographic regions and tropical storms. The purpose of this paper is to develop a formal theory of spatial relations for domains that include coincident entities. The core of the theory is a clear distinction between mereotopological relations, such as parthood and connection, and relative location relations, such as coincidence. To guide the (...) development of the formal theory, I construct mathematical models in which nontrivial relative location relations are defined. (shrink)

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 (...) linguistics, perceptual psychology, cate¬gorization and geographic information systems. Topological structures will be shown to play a central role in studies of naive physics not least in virtue of the fact that even well-attested departures from true physics on the part of common sense leave the topology and vectorial orientation of the underlying physical phenomena invariant: our common sense would thus seem to have a veridical grasp of the topology and broad general orientation of physical phenomena, both static and dynamic, even where it illegitimately modifies the relevant shape and metric properties. The implications of this and related insights for the methodology of psychology will be explored. (shrink)

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.

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 (...) the role of empty parts, in delivering a balanced and bounded metaphysics of naive space. (shrink)