Maureen Donnelly

A formal theory for spatial representation and reasoning in biomedical ontologies

OBJECTIVE The objective of this paper is to demonstrate how a formal spatial theory can be used as an important tool for disambiguating the spatial information embodied in biomedical ontologies and for enhancing their automatic reasoning capabilities. METHOD AND MATERIALS This paper presents a formal theory of parthood and location relations among individuals, called Basic Inclusion Theory (BIT). Since biomedical ontologies are comprised of assertions about classes of individuals (rather than assertions about individuals), we define parthood and location relations among classes in the extended theory Basic Inclusion Theory for Classes (BIT+Cl). We then demonstrate the usefulness of this formal theory for making the logical structure of spatial information more precise in two ontologies concerned with human anatomy: the Foundational Model of Anatomy (FMA) and GALEN. RESULTS We find that in both the FMA and GALEN, class-level spatial relations with different logical properties are not always explicitly distinguished. As a result, the spatial information included in these biomedical ontologies is often ambiguous and the possibilities for implementing consistent automatic reasoning within or across ontologies are limited. CONCLUSION Precise formal characterizations of all spatial relations assumed by a biomedical ontology are necessary to ensure that the information embodied in the ontology can be fully and coherently utilized in a computational environment. This paper can be seen as an important beginning step toward achieving this goal, but much more work along these lines is required.

A spatio-temporal ontology for geographic information integration

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.

Logical properties of foundational relations in bio-ontologies

OBJECTIVE We compare the advantages of specifying the semantics of foundational relations in bio-medical terminology systems using different types of formal deductive systems: first-order logic (FOL) and description logics (DLs). METHOD As our focus example, we use a terminology whose basic terms are supposed to designate proper parthood relations, subdivision relations, and surrounded-by relations. Each type of relation captures an important and distinct aspect of the spatial organization of anatomical structures: the general part-whole structure (proper parthood), the division of salient anatomical objects into discrete, tree-like structures (subdivision-of), and the nesting of anatomical objects into containers (surrounded-by). We show that all three types of relations are strict partial orderings (i.e., asymmetric and transitive). Ontologies whose purpose is to specify the semantics of terms referring to these types of relations must include axioms strong enough to formally distinguish among them. We compare the extent to which axioms characterizing proper parthood, subdivision, and surrounded-by relations can be represented in first-order logic and various description logics. CONCLUSIONS The development of bio-medical ontologies requires a rigorous formal analysis of foundational relations. Different kinds of formal tools may be used in this process. Ideally, an analysis in a highly expressive language, such as first-order logic, should be worked out in conjunction with analyses in less expressive but computationally tractable deductive systems such as description logics.

Spatial relations between classes of individuals

In the Spatial Data Transfer Standard and many other geographic standards and ontologies, we find statements such as (1) “waterfalls are parts of watercourses” and (2) “ecoregions of continental scale are parts of ecoregions of global scale”, etc. In these examples, the terms “waterfall”, “watercourse”, “ecoregion of scale X”, etc. refer to classes of individuals rather than to particular individuals. Since it is the purpose of these standards and ontologies to facilitate interoperability, it is important to give a clear semantics to statements like (1) and (2). For example, (1) should be understood to claim that every waterfall is part of some watercourse, but NOT that every watercourse has a waterfall as its part. In (2), by contrast, the term “part-of” has a stronger meaning: every ecoregion of continental scale is part of some ecoregion of global scale AND every ecoregion of global scale has some ecoregion of continental scale as a part. To overcome this kind of semantic heterogeneity, we propose a Mereotopology for Individuals and Classes (MIC) in which we define parthood, location, and connection relations among classes based on parthood, location, and connection relations between individuals. We then demonstrate the usefulness of this formal theory for making the logical structure of spatial information more precise. Although we focus here on the simplest and most pervasive of the spatial relations (parthood, location, and connection), the strategy employed in this paper can be used in analogous treatments of other kinds of relations among classes.

Modeling Principles and Methodologies - Spatial Representation and Reasoning

Spatial relations include mereological relations such as parthood and overlap, topological relations such as connectedness and one-pieceness, as well as location relations. The location and the arrangement of an anatomical structure within the human body can be further specified by means of relations that express spatial orderings in a qualitative way, e.g. superior, anterior, lateral, etc. In this chapter we give an overview of the various kinds of spatial relations and their properties. We particularly focus on properties of spatial relations that can be exploited for automated reasoning. We also discuss the distinction between so-called individual-level and type-level spatial relations.

Mereological vagueness and existential vagueness

It is often assumed that indeterminacy in mereological relations—in particular, indeterminacy in which collections of objects have fusions—leads immediately to indeterminacy in what objects there are in the world. This assumption is generally taken as a reason for rejecting mereological vagueness. The purpose of this paper is to examine the link between mereological vagueness and existential vagueness. I hope to show that the connection between the two forms of vagueness is not nearly so clear-cut as has been supposed.

A classification of spatio-temporal entities based on their location in space-time

We present an axiomatic theory of spatio-temporal entities based on the primitives spatial-region, part-of, and is-an-instance-of We provide a classification of spatio-temporal entities according to the number and kinds of regions at which they are located in spacetime and according to whether they instantiate or are instantiated at those regions The focus on location and instantiation at a location as the central notions of this theory makes it particularly appropriate for serving as a foundational ontology for geography and geographic information science.

The Moving Spotlight: An Essay on Time and Ontology, by Ross Cameron

and others as not. Brock preserves the inferences by accepting additional premises about realism as a theory (such as that it is deductively closed). In chapter 10, Amie L. Thomasson defends her ‘deflationary realism’ from the objection that the ontological claims it accepts should be understood as being uttered in pretence. The objection backfires, Thomasson argues. It leaves the objector—but not the deflationist—needing to articulate what more would be needed for there really to be fictional characters. In chapter 11, Anthony Everett and Timothy Schroeder propose that fictional characters are ideas that are had in devising ways to tell stories. They argue that ideas should be individuated in terms of their origins; but they aim to incorporate talk that seems to individuate ideas by their contents, by saying that ordinary practices of individuation are ‘interest relative, context sensitive, and in many instances simply sloppy’ [277]. Here I have doubts: interest relativity and context sensitivity are different from sloppiness. If judgments of what is what are genuinely to be evaluated relative to an interest, and if our interest is sometimes in contents, then it is not clear why individuation by content should be, as Everett and Schroeder suggest, misindividuation. This qualm does not, however, undermine the interest of Everett and Schroeder’s novel proposal. I enjoyed Fictional Objects very much. All of its chapters are rich in argument, creative in their ideas, and food for thought for anyone interested in fictionality and its relations to existence, possibility, thought, and language.

A Linguistic Account of Mereological Vagueness

Proponents of linguistic accounts of vagueness generally trace vagueness in mereological claims to imprecision in singular terms. The purpose of this chapter is to develop an alternative linguistic account of vague mereological claims. I propose that vagueness in ordinary mereological claims is typically due, not to imprecision in singular terms, but to imprecision in mereological terms such as the relational predicate “is part of.” Though my account is not problem-free, I think it is preferable to the standard linguistic account because it preserves important ordinary intuitions about objects. Moreover, my account is supported by the evident lack of rigor and specificity in our actual use of mereological vocabulary. I further suggest that my linguistic account of mereological vagueness might accommodate some intuitions motivating ontic accounts of vagueness while avoiding a troublesome commitment to indeterminacy in the world.