title: From Domains Towards a Logic of Universals: A Small Calculus for the Continuous Determination of Worlds
creator: Brillowski, Dr. Claus
subject: Language
subject: Dynamical Systems
subject: Semantics
subject: Syntax
subject: Logic
description: At the end of the 19th century, 'logic' moved from the discipline of philosophy to that of mathematics. One hundred years later, we have a plethora of formal logics. Looking at the situation form informatics, the mathematical discipline proved only a temporary shelter for `logic'. For there is Domain Theory, a constructive mathematical theory  which extends the notion of computability into the continuum and spans the  field of all possible deductive systems. Domain Theory  describes the space of data-types which computers can ideally compute -- and computation in terms of these types. Domain Theory is constructive but only potentially operational.  Here one particular operational model is derived from Domain Theory which consists of  `universals', that is, model independent operands and operators. With these universals, Domains (logical models) can be approximated and continuously determined. The universal data-types and rules derived from Domain Theory relate strongly to the first formal logic conceived on philosophical grounds, Aristotelian (categorical) logic. This is no accident.  For Aristotle, deduction was type-dependent and he too thought in term of type independent universal `essences'. This paper initiates the next `logical' step `beyond' Domain Theory  by reconnecting `formal logic' with its origin.
date: 2010-09-02
type: Preprint
type: NonPeerReviewed
format: application/pdf
identifier: http://cogprints.org/6948/1/SmallCalculus.pdf
identifier:   Brillowski, Dr. Claus  (2010) From Domains Towards a Logic of Universals: A Small Calculus for the Continuous Determination of Worlds.  [Preprint]     
relation: http://cogprints.org/6948/