The Monster Objection has often been considered one of the main reasons to explore non-standard mereological views, such as hylomorphism. Still, it has been rarely discussed and then only in a cursory fashion. This paper fills this gap by offering the first thorough assessment of the objection. It argues that different metaphysical stances, such as presentism and three- and four-dimensionalism, provide different ways of undermining the objection.

In the domain of ontology design as well as in Knowledge Representation, modeling universals is a challenging problem.Most approaches that have addressed this problem rely on Description Logics (DLs) but many difficulties remain, due to under-constrained representation which reduces the inferences that can be drawn and further causes problems in expressiveness. In mathematical logic and program checking, type theories have proved to be appealing but, so far they have not been applied in the formalization of ontologies. To bridge this gap, (...) we present in this paper a theory for representing ontologies in a dependently typed framework which relies on strong formal foundations including both a constructive logic and a functional type system. The language of this theory defines in a precise way what ontological primitives such as classes, relations, properties, etc., and thereof roles, are. The first part of the paper details how these primitives are defined and used within the theory. In a second part, we focus on the formalization of the role primitive. A review of significant role properties leads to the specification of a role profile and most of the remaining work details through numerous examples, how the proposed theory is able to fully satisfy this profile. It is demonstrated that dependent types can model several non-trivial aspects of roles including a formal solution for generalization hierarchies, identity criteria for roles and other contributions. A discussion is given on how the theory is able to cope with many of the constraints inherent in a good role representation. (shrink)

This paper presents an axiomatic formalization of a theory of top-level relations between three categories of entities: individuals, universals, and collections. We deal with a variety of relations between entities in these categories, including the sub-universal relation among universals and the parthood relation among individuals, as well as cross-categorial relations such as instantiation and membership. We show that an adequate understanding of the formal properties of such relations – in particular their behavior with respect to time – is critical for (...) geographic information processing. The axiomatic theory is developed using Isabelle, a computational system for implementing logical formalisms. All proofs are computer verified and the computational representation of the theory is available online. (shrink)

We propose an ontological theory that is powerful enough to describe both complex spatio-temporal processes and the enduring entities that participate therein. For this purpose we introduce the notion a directly depicting ontology. Directly depicting ontologies are based on relatively simple languages and fall into two major categories: ontologies of type SPAN and ontologies of type SNAP. These represent two complementary perspectives on reality and employ distinct though compatible systems of categories. A SNAP (snapshot) ontology comprehends enduring entities such as (...) organisms, geographic features, or qualities as they exist at some given moment of time. A SPAN ontology comprehends perduring entities such as processes and their parts and aggregates as they unfold themselves through some temporal interval. We give an axiomatic account of the theory of directly depicting ontologies and of the core parts of the metaontological fragment within which they are embedded. (shrink)

This essay is a response to Luis M. Augusto’s intriguing paper on the rift between mainstream and formal ontology. I will show that there are in fact two questions at issue here: 1. concerning the links between mainstream and formal approaches within philosophy, and 2. concerning the application of philosophy (and especially philosophical ontology) in support of information-driven research for example in the life sciences.

The pivotal role of the relation part-of in the description of living organisms is widely acknowledged. Organisms are open systems, which means that in contradistinction to mechanical artifacts they are characterized by a continuous flow and exchange of matter. A closer analysis of the spatial relations in biological organisms reveals that the decision as to whether a given particular is part-of a second particular or whether it is only contained-in the second particular is often controversial. We here propose a rule-based (...) approach which allows us to decide on the basis of well-defined criteria which of the two relations holds between two anatomical objects, given that one spatially includes the other. We discuss the advantages and limitations of this approach, using concrete examples from human anatomy. (shrink)