Thomas Bittner

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.

Biomedical ontologies: what part-of is and isn't

Mereological relations such as part-of and its inverse has-part are fundamental to the description of the structure of living organisms. Whereas classical mereology focuses on individual entities, mereological relations in biomedical ontologies are generally asserted between classes of individuals. In general, this practice leaves some basic issues unanswered: type constraints of mereological relations, e.g., concerning artifacts and biological entities, the relation between parthood and time, inferred parts and wholes as well as a delimitation of parthood against spatial inclusion. Furthermore, mereological relations can be asserted not only between physical objects but also between biological processes and medical procedures. We analyze these ambiguities and make suggestions for a standardization of mereological relations in biomedical ontologies.

A boundary-sensitive approach to qualitative location

Reasoning about the location of regions in 2-dimensional space is necessarily based on finite approximations to such regions. These finite approximations are often derived by describing how a region (the figure) relates to a frame of reference (the ground). The frame of reference generally consists of regions, or cells, forming a partition of the space under consideration. This paper presents a new approach to describing figure-ground relationships which is able to take account of how the figure relates to boundaries between cells as well as to their interiors. We also provide a general theory of how approximations to regions lead to approximations to operations on regions. This theory is applied to the case of our boundary-sensitive model of location. The paper concludes by indicating how interpreting boundaries in a more general sense should lead to a theory dealing with generalized partitions in which the cells may overlap. The applications of the theory developed here will include qualitative spatial reasoning, and should have practical relevance to geographical information systems.

Vagueness and Rough Location

This paper deals with the representation and the processing of information about spatial objects with indeterminate location like valleys or dunes (objects subject to vagueness). The indeterminacy of the location of spatial objects is caused by the vagueness of the unity condition provided by the underlying human concepts valley and dune. We propose the notion of rough, i.e., approximate, location for representing and processing information about indeterminate location of objects subject to vagueness. We provide an analysis of the relationships between vagueness of concepts, indeterminacy of location of objects, and rough approximations using methods of formal ontology. In the second part of the paper we propose an algebraic formalization of rough location, and hence, a formal method for the representation of objects subject to vagueness on a computer. We further define operations on those representations, which can be interpreted as union and intersection operations between those objects. The discussion of vagueness of concepts, indeterminacy of location, rough location and the relationships between these notions contributes to the theory about the ontology of geographic space. The formalization presented can provide the foundation for the implementation of vague objects and their location indeterminacy in GIS.

A Taxonomy of Granular Partitions

In this paper we propose a formal theory of granular partitions (ways of dividing up or sorting or mapping reality) and we show how the theory can be applied in the geospatial domain. We characterize granular partitions at two levels: as systems of cells, and in terms of their projective relation to reality. We lay down conditions of well-formedness for granular partitions, and we define what it means for partitions to project transparently onto reality in such a way as to be structure-preserving. We continue by classifying granular partitions along three axes, according to: (a) the degree to which a partition represents the mereological structure of the domain it is projected onto; (b) the degree of completeness and exhaustiveness with which a partition represents reality; and (c) the degree of redundancy in the partition structure. This classification is used to characterize three types of granular partitions that play an important role in spatial information science: cadastral partitions, categorical coverages, and the partitions involved in folk categorizations of the geospatial domain.

Stratified rough sets and vagueness

The relationship between less detailed and more detailed versions of data is one of the major issues in processing geographic information. Fundamental to much work in model-oriented generalization, also called semantic generalization, is the notion of an equivalence relation. Given an equivalence relation on a set, the techniques of rough set theory can be applied to give generalized descriptions of subsets of the original set. The notion of equivalence relation, or partition, has recently been significantly extended by the introduction of the notion of a granular partition. A granular partition provides what may be thought of as a hierarchical family of partial equivalence relations. In this paper we show how the mechanisms for making rough descriptions with respect to an equivalence relation can be extended to give rough descriptions with respect to a granular partition. In order to do this, we also show how some of the theory of granular partitions can be reformulated; this clarifies the connections between equivalence relations and granular partitions. With the help of this correspondence we then can show how the notion of hierarchical systems of partial equivalence classes relates to partitions of partial sets, i.e., partitions of sets in which not all members are known. This gives us new insight into the relationships between roughness and vagueness.

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.

The RNA Ontology RNAO: An ontology for integrating RNA sequence and structure data

Biomedical Ontologies integrate diverse biomedical data and enable intelligent data-mining and help translate basic research into useful clinical knowledge. We present the RNA Ontology (RNAO), an ontology for integrating diverse RNA data, including RNA sequences and sequence alignments, three-dimensional structures, and biochemical and functional data. For example, individual atomic resolution RNA structures have broader significance as representatives of classes of homologous molecules, which can differ significantly in sequence while sharing core structural features and common roles or functions. Thus, structural data gain value by being linked to homologous sequences in genomic data and databases of sequence alignments. Likewise, the value of genomic data is enhanced by annotation of shared structural features, especially when these can be linked to specific functions. Moreover, the significance of biochemical, functional and mutational analyses of RNA molecules are most fully understood when linked to molecular structures and phylogenies. To achieve these goals, RNAO provides logically rigorous definitions of the components of RNA primary, secondary and tertiary structure and the relations between these entities. RNAO is being developed to comply with the developing standards of the Open Biomedical Ontologies (OBO) Consortium. The RNAO can be accessed at http://code.google.com/p/rnao/.

Rough Sets in Approximate Spatial Reasoning

In spatial reasoning the qualitative description of relations between spatial regions is of practical importance and has been widely studied. Examples of such relations are that two regions may meet only at their boundaries or that one region is a proper part of another. This paper shows how systems of relations between regions can be extended from precisely known regions to approximate ones. One way of approximating regions with respect to a partition of the plane is that provided by rough set theory for approximating subsets of a set. Relations between regions approximated in this way can be described by an extension of the RCC5 system of relations for precise regions. Two techniques for extending RCC5 are presented, and the equivalence between them is proved. A more elaborate approximation technique for regions (boundary sensitive approximation) takes account of some of the topological structure of regions. Using this technique, an extension to the RCC8 system of spatial relations is presented.