Brillowski, Dr. Claus (2010) From Domains Towards a Logic of Universals: A Small Calculus for the Continuous Determination of Worlds. [Preprint]
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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 datatypes 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 datatypes 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 typedependent 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.
Item Type:  Preprint 

Keywords:  Logic, Aristotelian logic, Domain Theory, Computability, Datatypes, Modes of being, Universals, Topological Information Storage, Problem of Induction 
Subjects:  Computer Science > Language Computer Science > Dynamical Systems Linguistics > Semantics Linguistics > Syntax Philosophy > Logic 
ID Code:  6948 
Deposited By:  Brillowski, Dr Claus 
Deposited On:  13 Sep 2010 03:57 
Last Modified:  11 Mar 2011 08:57 
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