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 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.

Item Type: | Preprint |
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Keywords: | Logic, Aristotelian logic, Domain Theory, Computability, Data-types, 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 04:57 |

Last Modified: | 11 Mar 2011 08:57 |

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