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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."
altloc:
  - http://www.logike.info/resources/SmallCalculus.pdf
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creators_id:
  - brillowski@logike.info
creators_name:
  - family: Brillowski
    given: Claus
    honourific: Dr.
    lineage: ''
date: 2010-09-02
date_type: completed
datestamp: 2010-09-13 03:57:35
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dir: disk0/00/00/69/48
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eprintid: 6948
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keywords: 'Logic, Aristotelian logic, Domain Theory, Computability, Data-types, Modes of being,  Universals, Topological Information Storage, Problem of Induction'
lastmod: 2011-03-11 08:57:40
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referencetext: "Abramsky S. (2008), Information, Processes and Games, Philosophy of Information. \r\nAristotle (1984), The Complete Works of Aristotle: The Revised Oxford Translation, Ed. J.Barnes, Bollingen.\r\nClavel M. et al. (2007), All about Maude - A High-Performance Logical Framework. Available here: http://www.springerlink.com/openurl.asp?genre=issue&issn=0302-9743&volume=4350\r\nSextus Empiricus, Outlines of Pyrrhonism, Translation R.G. Burry.\r\nFrege G. (1977), Begriffsschrift und andere Aufsätze, Wiss. Buchges., Darmstadt.\r\nFriedman M. (2000), A Parting of the Ways: Carnap, Cassirer and Heidegger.\r\nGlashoff K. (2005), Aristotelian Syntax from a Computational-Combinatorial Point of View,\r\nAvailable here: http://www.logic.glashoff.net/Texte/reduction2.pdf\r\nGlashoff K. (2006), Zur Übersetzung der Aristotelischen Logik in die Prädikatenlogik, Available here: http://www.logic.glashoff.net/Texte/Manuscript_Nuernberg.pdf\r\nHeidegger M. (1939), Vom Wesen und Begriff der PHYSIS.\r\nHeidegger M. (1968), What is a Thing?\r\nHeidegger M. (1919/20), Die Grundprobleme der Phänomenologie.\r\nHeidegger M. (1929/30), Die Grundbegriffe der Metaphysik.\r\nHeidegger M. (1925/26), Logik: Die Frage nach der Wahrheit.\r\nJoseph HWB. (1916), An Introduction to Logic.\r\nKirk G.S. et al. (1983), The Presocratic Philosophers.\r\nLemmon E.J. (1971), Beginning Logic.\r\nMill JS. (1884), A System of Logic Ratiocinative and Inductive.\r\nPlotkin G. (1983), Domains, Department of Computer Science, University of Edinburgh. Available here: \r\nScott D. (1973), Models for Various Type-Free Calculi.\r\nScott D. (1982), Domains for Denotational Semantics.\r\nScott D. (1981), Lectures on a Mathematical Theory of Computation.\r\nStoy J.E. (1977), Denotational Semantics: The Scott-Strachey Approach to Programming Language\r\nTheory.\r\nTarski A. (1944), The Semantic Conception of Truth and the Foundations of Semantics. \r\nTurner J.L. &  McCluskey T.L. (1993), The Construction of Formal Specifications: An Introduction\r\nto the Model-Based and Algebraic Approaches. Available here: http://scom.hud.ac.uk/scomtlm/book.pdf\r\nWeihrauch K. (1987), Computability."
relation_type: []
relation_uri: []
reportno: ~
rev_number: 60
series: ~
source: ~
status_changed: 2010-09-13 03:57:34
subjects:
  - comp-sci-lang
  - comp-sci-mach-dynam-sys
  - ling-sem
  - ling-syntax
  - phil-logic
succeeds: ~
suggestions: ~
sword_depositor: ~
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title: 'From Domains Towards a Logic of Universals: A Small Calculus for the Continuous Determination of Worlds'
type: preprint
userid: 10921
volume: ~
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