Heinrich Herre

The concept of situation is crucial for many domain ontologies, particularly in complex fields such as biomedicine. For instance, work on the Cell Tracking Ontology (CTO) revealed that the notion of situation is fundamental for the adequate representation of cellular genealogies, which provide a detailed record of the lineage and development of cells over time. Related findings were observed in other biomedical use cases, such as surgical navigation, medical risk identification, and pregnancy care and complication prevention. The development of these applications heavily rests on the General Formal Ontology (GFO, version 1.0), which effectively represents situations. However, different terminologies and modeling variations have been used across these applications, leading to modifications and extensions of GFO. We aim to generalize the results from CTO and other GFO applications towards a systematic basis for situation modeling. The paper reviews four biomedical projects using GFO for situation modeling and discusses the GFO theory of situations, along with its underlying intuitions. Based on this, we introduce a family of ontology design patterns tailored to modeling situations, which can be challenging, as an optimal approach often depends on the specific use case and requirements. However, the range of approaches observed in real-world scenarios is sufficiently limited to allow for a systematic classification of the modeling methods, addressing various levels of detail. Therefore, the family of patterns aims at providing a toolbox for depicting situations at different granularities, including their participants, qualities, dynamics, and changes over time, rather than forcing a one-size-fits-all approach.

Although the ideas in Process and Reality are well-recognized by many scientists in various disciplines beyond philosophy, these investigations are focused on the formal interpretation of the notion of space in the context of mereotopology. Indeed, the notion of time is either neglected completely or understood as an abstraction from the four-dimensional existence of enduring objects. However, there is no elucidation of the notion of time beyond this existence. We introduce a monadic second order language to formalize the ultimate principles presupposed to Whitehead’s investigation, i.e., creativity, novelty and advance have been analyzed and reformulated as axioms. The models of the formulated theory are linear process structures, which are a special type of occurrence structures. The model-theoretic aspects of their theory are discussed in the present paper. Our fundamental theorem indicates that the worlds, which ground the knowledge of actual occasions, are ordered linearly and are equal for contemporaneous actual occasions, which implies a condition essential to the being of time.

General Ontological Language (GOL) is a formal framework for representing and building ontologies. The purpose of GOL is to provide a system of top-level ontologies which can be used as a basis for building domain-specific ontologies. The present paper gives an overview about the basic categories of the GOL-ontology. GOL is part of the work of the research group Ontologies in Medicine (Onto-Med) at the University of Leipzig which is based on the collaborative work of the Institute of Medical Informatics (IMISE) and the Institute for Computer Science (IfI). It represents work in progress toward a proposal for an integrated family of top-level ontologies and will be applied to several fields of medicine, in particular to the field of Clinical Trials.

Every domain-specific ontology must use as a framework some upper-level ontology which describes the most general domain-independent categories of reality. In the present paper we sketch a new type of upper-level ontology, and we outline an associated knowledge modelling language called GOL – for: General Ontological Language. It turns out that the upper-level ontology underlying well-known standard modelling languages such as KIF, F-Logic and CycL is restricted to the ontology of sets. In a set theory which allows Urelements, however, there will be ontological relations between these Urelements which the set-theoretic machinery cannot capture. In contrast to standard modelling and representation formalisms, GOL provides a machinery for representing and analysing such ontologically basic relations. GOL is thus a genuine extension of KIF and of similar languages. In GOL entities are divided into sets and Urelements, the latter being divided in their turn into individuals and universals. Foremost among the individuals are things or substances, tropes or moments, and situoids: entities containing facts as components.

Every domain-specific ontology must use as a framework some upper-level ontology which describes the most general, domain-independent categories of reality. In the present paper we sketch a new type of upper-level ontology, which is intended to be the basis of a knowledge modelling language GOL (for: 'General Ontological Language'). It turns out that the upper- level ontology underlying standard modelling languages such as KIF, F-Logic and CycL is restricted to the ontology of sets. Set theory has considerable mathematical power and great flexibility as a framework for modelling different sorts of structures. At the same time it has the disadvantage that sets are abstract entities (entities existing outside the realm of time, space and causality), and thus a set-theoretical framework should be supplemented by some other machinery if it is to support applications in the ripe, messy world of concrete objects. In the present paper we partition the entities of the real world into sets and urelements, and then we introduce several new ontological relations between these urelements. In contrast to standard modelling and representation formalisms, the concepts of GOL provide a machinery for representing and analysing such ontologically basic relations.

The objective of this research programme is to contribute to the establishment of the emerging science of Formal Ontology in Information Systems via a collaborative project involving researchers from a range of disciplines including philosophy, logic, computer science, linguistics, and the medical sciences. The re­searchers will work together on the construction of a unified formal ontology, which means: a general framework for the construction of ontological theories in specific domains. The framework will be constructed using the axiomatic-deductive method of modern formal ontology. It will be tested via a series of applications relating to on-going work in Leipzig on medical taxonomies and data dictionaries in the context of clinical trials. This will lead to the production of a domain-specific ontology which is designed to serve as a basis for applications in the medical field.

The General Formal Ontology (GFO) is a top-level ontology that is being developed at the University of Leipzig since 1999. Besides introducing some of the basic principles of the ontology, we expound axiomatic fragments of its formalization and present ontological models of several use cases. GFO is a top-level ontology that integrates objects and processes into a unified framework, in a way that differs significantly from other ontologies. Another unique selling feature of GFO is its meta-ontological architecture, which includes set theory into ontology and which accounts for its specific role in common representation approaches. The second level of that architecture starts from the distinction of categories and individuals, which forms the backbone of the world’s structure. Furthermore, GFO comprises several kinds of categories, among them universals and concepts, and it considers several ontological regions and levels. In the context of this special issue paper, we study five pre-determined use cases from the perspective of GFO. The results of these analyses yield insights into how the ontology treats several important notions. Very abridged, this covers material objects and their composition; roles and social entities; properties with their relations to objects and processes, and their changing; changes of processes, including a functional perspective; and, eventually, the nature and changing of concepts as well as terminology. A final part summarizes application projects that use GFO in various contexts.

A fundamental notion in a large part of mathematics is the notion of equicardinality. The language with Hartig quantifier is, roughly speaking, a first-order language in which the notion of equicardinality is expressible. Thus this language, denoted by LI, is in some sense very natural and has in consequence special interest. Properties of LI are studied in many papers. In [BF, Chapter VI] there is a short survey of some known results about LI. We feel that a more extensive exposition of these results is needed. The aim of this paper is to give an overview of the present knowledge about the language LI and list a selection of open problems concerning it. After the Introduction $(\S1)$ , in $\S\S2$ and 3 we give the fundamental results about LI. In $\S4$ the known model-theoretic properties are discussed. The next section is devoted to properties of mathematical theories in LI. In $\S6$ the spectra of sentences of LI are discussed, and $\S7$ is devoted to properties of LI which depend on set-theoretic assumptions. The paper finishes with a list of open problem and an extensive bibliography. The bibliography contains not only papers we refer to but also all papers known to us containing results about the language with Hartig quantifier. Contents. $\S1$ . Introduction. $\S2$ . Preliminaries. $\S3$ . Basic results. $\S4$ . Model-theoretic properties of $LI. \S5$ . Decidability of theories with $I. \S6$ . Spectra of LI- sentences. $\S7$ . Independence results. $\S8$ . What is not yet known about LI. Bibliography

Modeling functions is a key aspect of artifact design, including software engineering and business systems modeling, but it is likewise of fundamental importance in natural systems modeling, for example in modeling biological organisms. The Unified Modeling Language (UML), which originated from object-oriented software engineering, is nowadays a de facto standard for conceptual modeling and its current applications go far beyond software engineering. The paper investigates first to what extent UML is suited for modeling functions. We survey various approaches to function modeling with UML and identify their limitations. Based on the conducted analysis, we introduce a UML profile for function modeling, called the Function Modeling Language (FueL). FueL enables the modeling of the structure of functions, of relations between functions, such as function decomposition, as well as of function ascription, i.e., of relations linking functions with other types of entities. The main application field that we considered while developing FueL is bioinformatics. Nonetheless, the presented profile is domain-independent and is capable of modeling cross-domain systems. The profile has been tested on fragments of the Molecular Function Ontology, a sub-ontology of the Gene Ontology. In this connection the paper further demonstrates that the applications of FueL transcend the construction of new models, by showing how the profile aids restructuring and refactoring existing models.

Time is a pervasive notion of high impact in information systems and computer science altogether. Respective understandings of the domain of time are fundamental for numerous areas, frequently in combination with closely related entities such as events, changes and processes. The conception and representation of time entities and reasoning about temporal data and knowledge are thus significant research areas. Each representation of temporal knowledge bears ontological commitments concerning time. Thus it is important to base temporal representations on a foundational ontology that covers general categories of time entities. In this article we introduce and discuss two consecutive ontologies of time that have been developed for the top-level ontology General Formal Ontology. The first covers intervals, named chronoids, and time boundaries of chronoids, as a kind of time points. One important specialty of time boundaries is their ability to coincide with other time boundaries. The second theory extends the first one by additionally addressing time regions, i.e., mereological sums of chronoids. Both ontologies are partially inspired by ideas of Franz Brentano, especially from his writings about the continuum. In particular, we view continuous time intervals as a genuine phenomenon which should not be identified with intervals of real numbers. On these grounds the resulting ontologies allow for proposing novel contributions to several problematic issues in temporal representation and reasoning, among others, the Dividing Instant Problem and the problem of persistence and change. Following our general approach to ontology development, both ontologies are axiomatized as formal theories in first-order logic and are analyzed metalogically. We prove the consistency of both ontologies, and completeness and decidability for one. Moreover, standard time theories with points and intervals are covered by both theories.

Although the ideas in Process and Reality are well-recognized by many scientists in various disciplines beyond philosophy, these investigations are focused on the formal interpretation of the notion of space in the context of mereotopology. Indeed, the notion of time is either neglected completely or understood as an abstraction from the four-dimensional existence of enduring objects. However, there is no elucidation of the notion of time beyond this existence. We introduce a monadic second order language to formalize the ultimate principles presupposed to Whitehead’s investigation, i.e., creativity, novelty and advance have been analyzed and reformulated as axioms. The models of the formulated theory are linear process structures, which are a special type of occurrence structures. The model-theoretic aspects of their theory are discussed in the present paper. Our fundamental theorem indicates that the worlds, which ground the knowledge of actual occasions, are ordered linearly and are equal for contemporaneous actual occasions, which implies a condition essential to the being of time.

General Ontological Language (GOL) is a formal framework for representing and building ontologies. The purpose of GOL is to provide a system of top-level ontologies which can be used as a basis for building domain-specific ontologies. The present paper gives an overview about the basic categories of the GOL-ontology. GOL is part of the work of the research group Ontologies in Medicine (Onto-Med) at the University of Leipzig which is based on the collaborative work of the Institute of Medical Informatics (IMISE) and the Institute for Computer Science (IfI). It represents work in progress toward a proposal for an integrated family of top-level ontologies and will be applied to several fields of medicine, in particular to the field of Clinical Trials.