A Formal Theory of Substances, Qualities, and Universals

One of the tasks of ontology in information science is to support the classification of entities according to their kinds and qualities. We hold that to realize this task as far as entities such as material objects are concerned we need to distinguish four kinds of entities: substance particulars, quality particulars, substance universals, and quality universals. These form, so to speak, an ontological square. We present a formal theory of classification based on this idea, including both a semantics for the theory and a provably sound axiomatization

Non-Deterministic Kleene Coalgebras

In this paper, we present a systematic way of deriving (1) languages of (generalised) regular expressions, and (2) sound and complete axiomatizations thereof, for a wide variety of systems. This generalizes both the results of Kleene (on regular languages and deterministic finite automata) and Milner (on regular behaviours and finite labelled transition systems), and includes many other systems such as Mealy and Moore machines