creators_name: Brillowski, Claus
creators_id: brillowski@logike.info
type: preprint
datestamp: 2010-09-13 03:57:35
lastmod: 2011-03-11 08:57:40
metadata_visibility: show
title: From Domains Towards a Logic of Universals: A Small Calculus for the Continuous Determination of Worlds
subjects: comp-sci-lang
subjects: comp-sci-mach-dynam-sys
subjects: ling-sem
subjects: ling-syntax
subjects: phil-logic
full_text_status: public
keywords: Logic, Aristotelian logic, Domain Theory, Computability, Data-types, Modes of being,  Universals, Topological Information Storage, Problem of Induction
abstract: 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
date_type: completed
refereed: FALSE
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citation:   Brillowski, Dr. Claus  (2010) From Domains Towards a Logic of Universals: A Small Calculus for the Continuous Determination of Worlds.  [Preprint]     
document_url: http://cogprints.org/6948/1/SmallCalculus.pdf