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.

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.

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.

Process ontologies play key roles in semantic integration and decision support systems for applications in manufacturing, enterprise modeling and e- commerce. In this paper, we propose a methodology for the design and verification of domain-specific process ontologies that are extensions of generic process ontologies. This allows us to evaluate the correctness of process ontologies with respect to the class of intended models for their respective domains. Our approach is based on the correspondence between the effects of activities in the process ontology and the partial automorphisms of models of the underlying domain ontology. We then investigate in detail the process ontology for the domain of chains (sets of disjoint linear orderings) using this methodology.