--- 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 chapter: ~ commentary: ~ commref: ~ confdates: ~ conference: ~ confloc: ~ contact_email: ~ 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 department: ~ dir: disk0/00/00/69/48 edit_lock_since: ~ edit_lock_until: 0 edit_lock_user: ~ editors_id: [] editors_name: [] eprint_status: archive eprintid: 6948 fileinfo: /style/images/fileicons/application_pdf.png;/6948/1/SmallCalculus.pdf full_text_status: public importid: ~ institution: ~ isbn: ~ ispublished: ~ issn: ~ item_issues_comment: [] item_issues_count: 0 item_issues_description: [] item_issues_id: [] item_issues_reported_by: [] item_issues_resolved_by: [] item_issues_status: [] item_issues_timestamp: [] item_issues_type: [] 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 latitude: ~ longitude: ~ metadata_visibility: show note: ~ number: ~ pagerange: ~ pubdom: FALSE publication: ~ publisher: ~ refereed: FALSE 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: ~ sword_slug: ~ thesistype: ~ title: 'From Domains Towards a Logic of Universals: A Small Calculus for the Continuous Determination of Worlds' type: preprint userid: 10921 volume: ~