From Domains Towards a Logic of Universals: A Small Calculus for the Continuous Determination of Worlds

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

Full text available as:

PDF (with Hypertext)


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
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

References in Article

Select the SEEK icon to attempt to find the referenced article. If it does not appear to be in cogprints you will be forwarded to the paracite service. Poorly formated references will probably not work.

Abramsky S. (2008), Information, Processes and Games, Philosophy of Information.

Aristotle (1984), The Complete Works of Aristotle: The Revised Oxford Translation, Ed. J.Barnes, Bollingen.

Clavel M. et al. (2007), All about Maude - A High-Performance Logical Framework. Available here:

Sextus Empiricus, Outlines of Pyrrhonism, Translation R.G. Burry.

Frege G. (1977), Begriffsschrift und andere Aufsätze, Wiss. Buchges., Darmstadt.

Friedman M. (2000), A Parting of the Ways: Carnap, Cassirer and Heidegger.

Glashoff K. (2005), Aristotelian Syntax from a Computational-Combinatorial Point of View,

Available here:

Glashoff K. (2006), Zur Übersetzung der Aristotelischen Logik in die Prädikatenlogik, Available here:

Heidegger M. (1939), Vom Wesen und Begriff der PHYSIS.

Heidegger M. (1968), What is a Thing?

Heidegger M. (1919/20), Die Grundprobleme der Phänomenologie.

Heidegger M. (1929/30), Die Grundbegriffe der Metaphysik.

Heidegger M. (1925/26), Logik: Die Frage nach der Wahrheit.

Joseph HWB. (1916), An Introduction to Logic.

Kirk G.S. et al. (1983), The Presocratic Philosophers.

Lemmon E.J. (1971), Beginning Logic.

Mill JS. (1884), A System of Logic Ratiocinative and Inductive.

Plotkin G. (1983), Domains, Department of Computer Science, University of Edinburgh. Available here:

Scott D. (1973), Models for Various Type-Free Calculi.

Scott D. (1982), Domains for Denotational Semantics.

Scott D. (1981), Lectures on a Mathematical Theory of Computation.

Stoy J.E. (1977), Denotational Semantics: The Scott-Strachey Approach to Programming Language


Tarski A. (1944), The Semantic Conception of Truth and the Foundations of Semantics.

Turner J.L. & McCluskey T.L. (1993), The Construction of Formal Specifications: An Introduction

to the Model-Based and Algebraic Approaches. Available here:

Weihrauch K. (1987), Computability.


Repository Staff Only: item control page