TY - GEN
ID - cogprints6948
UR - http://cogprints.org/6948/
A1 - Brillowski, Dr. Claus
TI - From Domains Towards a Logic of Universals: A Small Calculus for the Continuous Determination of Worlds
Y1 - 2010/09/02/
N2 - 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.
AV - public
KW - Logic
KW - Aristotelian logic
KW - Domain Theory
KW - Computability
KW - Data-types
KW - Modes of being
KW - Universals
KW - Topological Information Storage
KW - Problem of Induction
ER -