Quantities and units of measure provide an important means by which intelligent agents interact with the physical world. Although multiple ontologies for quantities and units of measure have been proposed within the Applied Ontology community, they often incorporate questionable ontological commitments. Quantities are combined using notions of dimensional analysis that often conflate the combination of units with algebraic operations on real numbers. In this paper, we present an alternative approach that shifts the focus to the connection between kinds of measurements associated with a unit and the physical objects and processes that are being measured. One of the key features of this approach is that it makes minimal ontological commitments with respect to the TUpper upper ontology – the only new classes that are introduced are the classes for kinds of measures and associated units. We propose axiomatizations of the intended semantics for combining measurements, and the correct axiomatization of the relationship between the quantities and units of measure and the existing upper ontology.

Classical mereology is based on the assumption that any two underlapping elements have a sum, yet there are many domains (such as manufacturing assemblies, molecular structure, gene sequences, and convex time intervals) in which this assumption is not valid. In such domains, mereological sums must be connected objects. However, there has been little work in providing an axiomatization of such a mereology. Based on the observation that the underlying structures in these domains are represented by graphs, we propose a new mereotopology that axiomatizes the connected induced subgraph containment ordering for a graph, and then identify an axiomatization of the mereology that is a module of the mereotopology.

The near ubiquity of family relationship ontologies in the Semantic Web has brought on the question of whether any formal analysis has been done in this domain. This paper examines kinship relationships that are normally overlooked in formal analyses of domain-specific ontologies: how are such ontologies verified and validated? We draw inspiration from existing work done in anthropology, where attempts have been made to formally model kinship as atemporal algebraic models. Based on these algebraic models, we provide an ontology for kinship written in first-order logic and demonstrate how the ontology can be used to validate definitions found in Canadian legal laws and data collection documentation.

Multiple ontologies for units of measure have been proposed within the Applied Ontology community, and all of these ontologies introduce an array of new classes based on supposed distinctions between quantities, quantity kinds, and measures. Units are combined using notions of dimensional analysis that often conflate the combination of units with algebraic operations on real numbers. In this paper we present an alternative approach that shifts the focus to the connection between the units of measure and the physical objects and processes that are being measured. One of the key features of this approach is that it makes minimal ontological commitments with respect to the TUpperWare upper ontology - the only new classes that are introduced are the classes for the units of measure. We propose correct and complete axiomatizations for combining units of measure, and the correct axiomatization of the relationship between the units of measure and the existing upper ontology.

This paper outlines the reductive modularization and verification of the Descriptive Ontology for Linguistic and Cognitive Engineering (DOLCE). The ontology makes distinctions between enduring and perduring entities which is reflected in the resulting reductive modules, in contrast to previous work done to generate a consistency proof for DOLCE. We present our approach to verify DOLCE with mathematical theories in the Common Logic Ontology Repository (COLORE), and describe how the ontological commitments made by the authors of DOLCE have affected the resulting verification and reductive modularization.

This paper explores an alternative vision for upper ontologies which is more effective at facilitating the sharability and reusability of ontologies. The notion of generic ontologies is characterized through the formalization of ontological commitments and choices. Ontology repositories are used to modularize ontologies so that any particular upper ontology is equivalent to the union of a set of generic ontologies. In this way, upper ontologies are not replaced but rather integrated with other theories in the ontology repository.

The field of medicinal chemistry involves the design, synthesis, and development of new drugs that can be further enhanced with the application of ontologies. In this paper, we discuss the need for a molecular structure ontology to aid us in the task of drug discovery. We outline a requirements-driven approach that guides us in the design of the Molecular Structure Ontology (MoSt) by which we represent atoms, bonds, functional groups, and molecules as things in the ontology. Finally, we demonstrate how the ontology can be used to axiomatize small molecules like Daraprim.

Modules of a logical theory are subtheories that are conservatively extended by the theory. There are, on the other hand, subtheories that are not contained in any proper module of the theory, which we refer to as the residue of the theory. In this paper, we characterize properties of residues and explore their role in ontology modularization. We discuss that there are ontological commitments that cannot be captured by modules of a theory and must be axiomatized by residues. We observe that sentences in the residue of a theory eliminate some possible combinations of models of modules of the theory. In that sense, ontological commitments that are captured by residues basically determine how arbitrary models of modules must be combined.

In this paper, we examine techniques used to merge the upper ontologies of the Process Specification Language (PSL) and the Descriptive Ontology for Linguistic and Cognitive Engineering (DOLCE) ontologies. In particular, we focus on the parts of these two ontologies relevant to the commonsense notion of participation as a relation between objects, activities, and time. We discuss the obstacles faced to formalize the relationships between these ontologies and provide an overview of the methodology undertaken to bridge the ontologies together. New ontologies are introduced to bring the PSL and DOLCE ontologies together to allow us to specify the mappings between them. We illustrate how ontology verification is used to show faithful interpretations between the two upper ontologies. We also explore applications of ontology transfer between a mathematical ontology and an upper ontology as an additional means of specifying bridges between ontologies.

Semantic integration remains a challenge, but it is particularly problematic in areas such as e-commerce, where ontologies are either nonexistent or have lightweight axiomatizations. In this paper we present a case study that examines how two weak ontologies can be mapped together in the e-commerce setting. We also examine the role that upper-level interlingua ontologies can play in the development of ontology mappings.

In this paper, we examine the relationships between the axiomatization of participation in two upper ontologies, the Process Specification Language (PSL) and the Descriptive Ontology for Linguistic and Cognitive Engineering (DOLCE).We discuss the obstacles faced to formalize the relationships between these ontologies and provide an overview of the methodology undertaken to merge the ontologies together. We introduce new ontologies that serve to bridge the PSL and DOLCE ontologies together to allow us to specify the mappings between them. We illustrate how ontology verification is used to show faithful interpretations between the two upper ontologies.

This paper explores an alternative vision for upper ontologies which is more effective at facilitating the sharability and reusability of ontologies. The notion of generic ontologies is characterized through the formalization of ontological commitments and choices. Ontology repositories are used to modularize ontologies so that any particular upper ontology is equivalent to the union of a set of generic ontologies. In this way, upper ontologies are not replaced but rather integrated with other theories in the ontology repository.

The notion of participation as a relation between objects, activities, and time has been axiomatized in various ontologies. In this paper, we focus on three of these ontologies – PSL-Core, Gangemi’s axioms, and DOLCE. We provide a verification of these participation ontologies by introducing ontologies for new classes of mathematical structures known as incidence bundles and incidence foliations. The new mathematical ontologies serve as reusable ontology design patterns for participation, and also are the basis for mappings between the different participation ontologies. Finally, we illustrate the concept of ontology transfer through the use of these ontology design patterns.