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.

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.

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 (...) (IMISE) and the Institute for Computer Science (IfI). It represents work in progress toward a proposal for an integrated family of top-level ontologies and will be applied to several fields of medicine, in particular to the field of Clinical Trials. (shrink)

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 (...) boundary is treated in detail and shown to be essentially affected by mereological considerations. More precisely, the concept of boundary turns out to be realizable in a variety of different mereologically grounded versions. In particular, every part K of a Heyting algebra H gives rise to a well-behaved K-relative boundary operator. (shrink)

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.

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, (...) such as morphological essentialism (an object cannot change shape) and locative essentialism (an object cannot change position) are also examined. (shrink)

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. (...) pose any insuperable problem for constructivism, and that constructivism may have a useful new perspective to offer on physics. (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)

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 (...) geographic information processing. The axiomatic theory is developed using Isabelle, a computational system for implementing logical formalisms. All proofs are computer verified and the computational representation of the theory is available online. (shrink)

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.

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 (...) examples, but the concept of niche should be understood as being, like concepts such as part, boundary, and location, a structural concept that is applicable in principle to a wide range of different domains. (shrink)

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 (...) view that Gestalt psychology and experimental phenomenology provide a contribution to the research into perception by the construction of phenomenological models for an ecologically meaningful interpretation of the empirical evidence and the hypothetical constructs of the natural image research within the visual neuroscience. A formal framework for the phenomenological models is proposed, wherein Gestalt theoretical principles and empirical evidence are represented in terms of topological properties and relationships, which account for the order and structures that make the environment accessible to observers at a relevant behavioural level. It is finally argued that these models allow us to evaluate the principles and the empirical evidence of various natures which are integrated from different fields into the research into perception, and in particular into visual neurosciences. (shrink)

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)

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 (...) the idea of non-standard geographies, which may be associated with geography under a classical conception in the same sense in which non-standard logics are associated with classical logic. (shrink)

An overview of contemporary part-whole theories, with reference to both their axiomatic developments and their philosophical underpinnings.

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.

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.

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 (...) the Minimalist View: An element in the field of a part-whole relation is to be included in an inventory of the world if and only if it does not overlap any distinct element that is itself included in the inventory. (shrink)

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 (...) specific conditions, ontologies can be defined in terms of systems in which wholes inherit information from its parts. In this article, we describe how part-whole subsumption and, then, meronymic inheritance can be used to deal with type mismatch and metonymic interpretation of polysemous nouns. For this purpose, we attempt to merge old assumptions from both formal ontology and lexical semantics into a homogeneous framework. (shrink)

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 (...) intuitions about wholes. (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.

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 (...) in the drawer. Ergo *there is a hole in the drawer”. (shrink)

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, (...) but the concept of niche should be understood as being, like concepts such as part, boundary, and location, a structural concept that is applicable in principle to a wide range of different domains. (shrink)

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.

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 (...) is also proposed. Then we show how this can be interpreted for spatial reasoning by using qualitative symbolic representations of spatial relationships derived from mathematical morphology. This allows to establish some links between numerical and symbolic representations of spatial knowledge. (shrink)

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 (...) conscious subject imposes a requirement of topological integrity. (shrink)

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 (...) element in the field of a part‐whole relation is to be included in an inventory of the world if, and only if, it does not overlap any other element that is itself included in the inventory. As it turns out, a clarification of this view involves both a defense of mereological extensionality and an account of the topological distinction between detached and undetached parts. (shrink)