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A Dynamic Theory of Ontology

A diagrammatic approach to Hopf monads

Given a Hopf algebra in a symmetric monoidal category with duals, the category of modules inherits the structure of a monoidal category with duals. If the notion of algebra is replaced with that of monad on a monoidal category with duals then Bruguieres and Virelizier showed when the category of modules inherits this structure of being monoidal with duals, and this gave rise to what they called a Hopf monad. In this paper it is shown that there are good diagrammatic descriptions of dinatural transformations which allows the three-dimensional, object-free nature of their constructions to become apparent.

Action concepts for describing organised interaction

The main aim of this paper is to propose a set of action concepts useful for describing organised interaction. These action concepts focus on two distinctions: the distinction between direct and indirect action, and the distinction between successful and not necessarily successful action. The formal characterisation of these concepts is given by means of modal logic, following the same tradition in the logical characterisation of act descriptions as employed by Kanger (1972) and Porn (1970). The modal action operators proposed are also combined with a deontic logic and a conditional logic, in order to illustrate their application to the analysis of some simple organisations. The focus of interest is on the notion of transmission of agency, and on the characterisation of the conditions under which an organisation recognises that an agent has fulfilled the responsibilities assigned to him.

Sebastjan Vörös on Twitter

“"Here islands of great order coexist with surroundings of even greater disorder. - Is that a metaphor you can live with?" 3/3”

Action concepts for describing organised interaction

The main aim of this paper is to propose a set of action concepts useful for describing organised interaction. These action concepts focus on two distinctions: the distinction between direct and indirect action, and the distinction between successful and not necessarily successful action. The formal characterisation of these concepts is given by means of modal logic, following the same tradition in the logical characterisation of act descriptions as employed by Kanger (1972) and Porn (1970). The modal action operators proposed are also combined with a deontic logic and a conditional logic, in order to illustrate their application to the analysis of some simple organisations. The focus of interest is on the notion of transmission of agency, and on the characterisation of the conditions under which an organisation recognises that an agent has fulfilled the responsibilities assigned to him.

A diagrammatic approach to Hopf monads

Given a Hopf algebra in a symmetric monoidal category with duals, the category of modules inherits the structure of a monoidal category with duals. If the notion of algebra is replaced with that of monad on a monoidal category with duals then Bruguieres and Virelizier showed when the category of modules inherits this structure of being monoidal with duals, and this gave rise to what they called a Hopf monad. In this paper it is shown that there are good diagrammatic descriptions of dinatural transformations which allows the three-dimensional, object-free nature of their constructions to become apparent.