The General Formal Ontology 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. (shrink)

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. (shrink)

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. (shrink)

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. (shrink)

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. (shrink)

The aim of the present paper is to analyse compactness properties of nonmonotonic inference operations within the framework of model theory. For this purpose the concepts of a deductive frame and its semantical counterpart, a semantical frame are introduced. Compactness properties play a fundamental in the study of non-monotonic inference, and in the paper several new versions of compactness are studied.

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. (shrink)

A major strategy to reduce transport congestion and other social costs of transport is to ensure that travellers make the best decisions, based on real time information. A wide range of technological systems have been developed to provide this information, but little is known about how travellers actually respond to it. This book offers an overview of various transport telematics options and provides an appropriate methodological framework, followed by a presentation of results from actual applications of these telematics systems from (...) a range of European countries in various transport sectors. The empirical results are supplemented by analytical models and geographic information systems representations with a view on generalizing these findings and identifying the key parameters which determine user response. (shrink)