Processes are fundamental to enterprises, serving as significant engines of optimization and analysis. Understanding business processes is critical, yet integrating formal process ontologies with enterprise data and workflows remains difficult. We refer to this specific kind of ontology application, intended for practitioners working with enterprise data, as operational realization. The varied ontological commitments and highly expressive representation languages of process ontologies create barriers for operational realization, including issues of decidability, a lack of tooling, and operational constraints. This paper presents an architecture for the operational realization of process ontologies, driven by process mining needs. A key aspect of the architecture is the formalization of ontological commitments in tasks like data cleaning and analysis, which rely on implicit assumptions embedded in the interpretation of process data. Our approach builds on existing methodologies, notably ontology-based data access (OBDA), while going further by encoding domain knowledge required to interpret and reason with process data. This structure moves beyond an A-Box and T-Box distinction, explicitly capturing how the process ontology, domain data, and supporting data interpretation theories enable complex process reasoning. By structuring the dynamics of a process ontology, domain data, process data theories, and by characterizing reasoning scenarios, our approach provides a pragmatic foundation for integrating process ontologies into data-driven process workflows. We demonstrate this architecture with real enterprise data, challenge problems, and scenarios already widely used for benchmarking in process mining.

Space, time, objects, and events are fundamental concepts in ontologies. For substantivalists that believe entities are located at regions (space or spacetime), a key issue to address is the relationship between entities and their located regions. There is rich literature on the ontologies of location and mereology of material objects, as well as their philosophical foundations, but relatively little on events and their location. Most existing event ontologies provide little beyond the signatures and simply associate an event entity to space and time. In this study, we propose a new location ontology for events that formalize the relationship between events and spacetime, where events and spacetime maintain their own mereologies. We also make ontological commitments to support the mereological harmony of events and spacetime and provide the rationale and axiomatization of these commitments.

Within knowledge representation in artificial intelligence, a first-order ontology is a theory in first-order logic that axiomatizes the concepts in some domain. Ontology verification is concerned with the relationship between the intended models of an ontology and the models of the axiomatization of the ontology. In particular, we want to characterize the models of an ontology up to isomorphism and determine whether or not these models are equivalent to the intended models of the ontology. Unfortunately, it can be quite difficult to characterize the models of an ontology up to isomorphism. In the first half of this article, we review the different metalogical relationships between first-order theories and identify which relationship is needed for ontology verification. In particular, we will demonstrate that the notion of logical synonymy is needed to specify a representation theorem for the class of models of one first-order ontology with respect to another. In the second half of the article, we discuss the notion of reducible theories and show we can specify representation theorems by which models are constructed by amalgamating models of the constituent ontologies.

In recent years there has been a resurgence of interest in our community in the shape analysis of 3D objects repre-sented by surface meshes, their voxelized interiors, or surface point clouds. In part, this interest has been stimulated by the increased availability of RGBD cameras, and by applications of computer vision to autonomous driving, medical imaging, and robotics. In these settings, spectral co-ordinates have shown promise for shape representation due to their ability to incorporate both local and global shape properties in a manner that is qualitatively invariant to iso-metric transformations. Yet, surprisingly, such coordinates have thus far typically considered only local surface positional or derivative information. In the present article, we propose to equip spectral coordinates with medial (object width) information, so as to enrich them. The key idea is to couple surface points that share a medial ball, via the weights of the adjacency matrix. We develop a spectral feature using this idea, and the algorithms to compute it. The incorporation of object width and medial coupling has direct benefits, as illustrated by our experiments on object classification, object part segmentation, and surface point correspondence.

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.

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 expanding use of information systems in industrial and commercial settings has increased the need for interoperation between software systems. In particular, many social, industrial, and business information systems require a common basis for a seamless exchange of complex process information. This is, however, inhibited, because different systems may use distinct terminologies or assume different meanings for the same terms. A common solution to this problem is to develop logical theories that act as an intermediate language between different parties. In this article, we characterize a class of activities that can act as intermediate languages between different parties in those cases. We show that for each domain with finite number of elements there exists a class of activities, we called canonical activities, such that all possible changes within the domain can be represented as a sequence of occurrences of those activities. We use an algebraic structure for representing change and characterizing canonical activities, which enables us to abstract away domain-dependent properties of processes and activities, and demonstrate general properties of formalisms required for semantic integration of dynamic information systems.

Particular types are designated in this paper as types dependent on an individual, such as SpouseOfHenryVIII dependent on HenryVIII. Other notable possibilities include car models, biological species, and various geological formations. A characterization and formal representation is provided for particular types that (1) introduces particular dependence between a type and an individual; (2) is grounded in this dependence and some defining relation for the type; and (3) provides a multi-level ontology pattern, using lakes as exemplars. This expands the range of types available to geographical ontology and beyond.

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.

RCC8 is a set of eight jointly exhaustive and pairwise disjoint binary relations representing mereotopological relationships between ordered pairs of individuals. Although the RCC8 relations were originally presented as defined relations of Region Connection Calculus (RCC), virtually all implementations use the RCC8 Composition Table (CT) rather than the axioms of RCC. This raises the question of which mereotopology actually underlies the RCC8 composition table. In this paper, we characterize the algebraic and mereotopological properties of the RCC8 CT based on the metalogical relationship between the first-order theory that captures the RCC8 CT and Ground Mereotopology (MT) of Casati and Varzi. In particular, we show that the RCC8 theory and MT are relatively interpretable in each other. We further show that a nonconservative extension of the RCC8 theory that captures the intended interpretation of the RCC8 relations is logically synonymous with MT, and that a conservative extension of MT is logically synonymous with the RCC8 theory. We also present a characterization of models of MT up to isomorphism, and explain how such a characterization provides insights for understanding models of the RCC8 theory.

Allen's interval algebra is a set of thirteen jointly exhaustive and pairwise disjoint binary relations representing temporal relationships between pairs of timeintervals. Despite widespread use, there is still the question of which time ontology actually underlies Allen's algebra. Early work specified a first-order ontology that can interpret Allen's interval algebra; in this paper, we identify the first-order ontology that is logically synonymous with Allen's interval algebra, so that there is a one-to-one correspondence between models of the ontology and solutions to temporal constraints that are specified using the temporal relations. We further prove a representation theorem for the ontology, thus characterizing its models up to isomorphism.

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.

The reuse of ontologies is critical to their value as a means of knowledge representation. Unfortunately, reuse also still poses a considerable challenge for the ontological community. One reason for this is the lack of a formal definition of reuse. How can we attempt to perform or even assist this sort of ontology design, if we have no clear understanding of what constitutes reuse, and what does not? In this work we aim to remedy this situation by providing a formal definition of the concepts of reuse and reusability. Beyond providing a clear understanding of these concepts, part of the resulting definition is a characterization of the operations of reuse that can be leveraged to determine how a given ontology(s) must be reused to satisfy some specified requirements. This serves not only to provide direction for the task of reuse, but also to assess the implications of reusing an ontology(s), a priori. Collectively, the solutions presented in this paper serve as a major step in improving the current state of reuse.

Many software systems rely on ontologies for semantic interoperation. However, ontologies which admit unintended models might cause misunderstandings that hinder interoperability because their vocabularies are ambiguously defined. Foundational ontologies, such as SUMO, provide rich characterizations for general concepts that underly every knowledge representation enterprise. Those ontologies are intended to be broadly reused as a reference for semantics. Ontology verification is the process by which a theory is checked to rule out unintended models by means of further axiomatization, and characterize missing intended ones. In this paper, we verify the subtheory of core temporal concepts of the SUMO foundational ontology and relate its axiomatization via ontology mapping with other time ontologies, the foundational ontology DOLCE, and the generic ontology PSL. As a result, we propose the addition of some missing axioms that we have identified during our verification task, and the correction of others.

Upper-level ontologies provide an account of the most basic, domain-independent, existing entities, such as time, space, objects, and processes. Ontology verification is the process by which a theory is checked to rule out unintended models, and possibly characterize missing intended ones. In this paper, we verify the core characterization of mereotopology of the Suggested Upper Merged Ontology (SUMO), and the mereology of the Descriptive Ontology for Linguistic and Cognitive Engineering (DOLCE), while relating their axiomatizations via ontology mapping. As a result, we propose the correction and addition of some axioms to the analyzed theories which eliminate unintended models and characterize missing ones. In addition, we show by formal means which is the relation existing between the axiomatization of mereology in both upper-level ontologies, and make available a modular representation in first-order logic of the SUMO characterization of mereotopology.

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.

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.

Material-spatial interdependence (mat-dep) is a type of dependence in which the physical extents of two entities are necessarily and mutually contingent, e.g. an object and its matter, or a hole and its host. Such dependence is commonly found amongst arrangements of physical entities, particularly in models of the natural environment. In this paper, we analyze and formally characterize mat-dep, and show how it augments the physical characterization of the containment, constitution, and hosting relations, primarily for development of a hydro ontology.

Ontology verification is concerned with the relationship between the intended structures for an ontology and the models of the axiomatization of the ontology. The verification of a particular ontology requires characterization of the models of the ontology up to isomorphism and a proof that these models are equivalent to the intended structures for the ontology. In this paper we consider the verification of three time ontologies (first introduced by Hayes in his Catalog of Temporal Theories) that axiomatize both time points and time intervals together with the relationships between them. We identify axioms that are missing from these ontologies and provide a complete account of the metatheoretic relationships between the ontologies.

In this paper we show how the relationships between first-order ontologies within a repository can be used to support ontology verification. We discuss the use of representation theorems and classification theorems to characterize the models of an ontology, and then show how such results can be obtained from notions such as relative interpretation.

In this paper, the UML activity diagrams are first defined graph-theoretically, with an adoption of the concepts of Petri nets tokens. The semantics of activity diagrams is further axiomatized as a logical action theory called SCAD. Example applications of SCAD are also given.

Abstract: Process modeling is ubiquitous in business and industry. While a great deal of effort has been devoted to the formal and philosophical investigation of processes, surprisingly little research connects this work to real world process modeling. The purpose of this paper is to begin making such a connection. To do so, we first develop a simple mathematical model of activities and their instances based upon the model theory for the NIST Process Specification Language (PSL), a simple language for describing these entities, and a semantics for the latter in terms of the former, and a set of axioms for the semantics based upon the NIST Process Specification Language (PSL). On the basis of this foundation, we then develop a general notion of a process model, and an account of what it is for such a model to be realized by a collection of events.