Axiomatic Formal Ontology

Axiomatic Formal Ontology is a fairly comprehensive systematic treatise on general metaphysics. The axiomatic method is applied throughout the book. Its main theme is the construction of a general non-set-theoretical theory of intensional entities. Other important matters discussed are the metaphysics of modality, the nature of actual existence, mereology and the taxonomy of entities.

The book discusses the fate of universality and a universal set in several set theories. The book aims at a philosophical study of ontological and conceptual questions around set theory. Set theories are ontologies. They posit sets and claim that these exhibit the essential properties laid down in the set theoretical axioms. Collecting these postulated entities quantified over poses the problem of universality. Is the collection of the set theoretical entities itself a set theoretical entity? What does it mean if it is, and what does it mean if it is not? To answer these questions involves developing a theory of the universal set. We have to ask: Are there different aspects to universality in set theory, which stand in conflict to each other? May inconsistency be the price to pay to circumvent ineffability? And most importantly: How far can axiomatic ontology take us out of the problems around universality?

Formal ontology combines two ideas, one originating with Husserl, the other with Frege: that of ontology of the formal aspects of all objects, irrespective of their particular nature, and ontology pursued by employing the tools of modern formal disciplines, notably logic and semantics. These two traditions have converged in recent years and this is the first collection to encompass them as a whole in a single volume. It assembles essays from authors around the world already widely known for their work in formal ontology, and illustrates that through the application of formal methods the ancient discipline of ontology may be put on a firm methodological basis. The essays not only illuminate the nature of ontology and its relation to other areas, in language, logic and everyday life, but also demonstrate that common issues from the analytical and phenomenological traditions may be discussed without ideological barriers. Audience: advanced students of and specialists in philosophy, linguistics, cognitive science, computer science, database engineering.

Main description: The book discusses the fate of universality and a universal set in several set theories. The book aims at a philosophical study of ontological and conceptual questions around set theory. Set theories are ontologies. They posit sets and claim that these exhibit the essential properties laid down in the set theoretical axioms. Collecting these postulated entities quantified over poses the problem of universality. Is the collection of the set theoretical entities itself a set theoretical entity? What does it mean if it is, and what does it mean if it is not? To answer these questions involves developing a theory of the universal set. We have to ask: Are there different aspects to universality in set theory, which stand in conflict to each other? May inconsistency be the price to pay to circumvent ineffability? And most importantly: How far can axiomatic ontology take us out of the problems around universality?

Formal Ontology in Information Systems (FOIS) is the flagship conference of the International Association for Ontology and its Applications, a non-profit organization promoting interdisciplinary research and international collaboration at the intersection of philosophical ontology, linguistics, logic, cognitive science, and computer science. This book presents the 11 papers accepted for the 12th edition of FOIS. The conference was held from 13-17 September 2021 in Bozen-Bolzano, Italy, as a hybrid event with some participants attending on-site in Bolzano and others attending virtually online. The papers are divided into 3 sections and cover a wide range of topics: (1) Foundations, addressing fundamental issues; (2) Applications and Methods, presenting novel uses, systems, tools, and approaches; and (3) Domain Ontology, describing well-formed ontologies in particular subject areas.

FOIS is the flagship conference of the International Association for Ontology and its Applications, a non-profit organization which promotes interdisciplinary research and international collaboration at the intersection of philosophical ontology, linguistics, logic, cognitive science, and computer science, as well as in the applications of ontological analysis to conceptual modeling, knowledge engineering, knowledge management, information-systems development, library and information science, scientific research, and semantic technologies in general. This volume presents the 17 papers accepted for the 11th Formal Ontology in Information Systems conference (FOIS 2020). These papers cover a broad range of topics and are organized into 5 groups. Foundations is dedicated to the general ontological decisions providing a foundation for any ontology, both from a philosophical perspective and with an emphasis on applications. Social Entities is dedicated to the ontological analysis and formalization of various social entities, including secrets, legal theories, decisions, kinship, and cultural heritage. The papers in Intentionality and Embodiment analyze aspects of an agent's intentions, beliefs and desires, as well as the embodiment of functional relations. The section on Parts and Wholes is dedicated to mereology as well as the mereological analysis of certain types of entities (e.g., pluralities, information entities, and computer programs). Lastly, the papers in Methods are about ontology evaluation and use. Altogether, the papers reflect traditional FOIS themes with perhaps a greater emphasis on social and agent aspects, and will be of interest to all those whose work involves ontology and its applications.

Theories about the ontological structure of the world have generally been described in informal, intuitive terms. This book offers an account of the general features and methodology of formal ontology. The book defends conceptual realism as the best system to adopt based on a logic of natural kinds. By formally reconstructing an intuitive, informal ontological scheme as a formal ontology we can better determine the consistency and adequacy of that scheme.

Scientific literature on particular themes in ontology is extremely abundant, but it is often very hard for freshmen or sophomores to find a red thread between the various proposals. This text is an opinionated introduction, a preliminary text to research in ontology from the so called standard approach to ontological commitment, that is from the particular point of view that connects ontological questions to quantificational questions. It offers a survey of this viewpoint in ontology together with their possible applications through a broad array of examples and open problems and, at the same time, essential references to the classics of philosophy, so as to allow non-specialists to understand the terms and analysis procedures characterizing the discipline. Its result is a wide-ranging overview of the issued tackled by ontology, with a particular focus on the most relevant problems of contemporary debate (categorial taxonomies, nonexistent objects, case studies of ontological debates in specific fields of knowledge).