?url_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Adc&rft.title=From+Domains+Towards+a+Logic+of+Universals%3A+A+Small+Calculus+for+the+Continuous+Determination+of+Worlds&rft.creator=Brillowski%2C+Dr.+Claus&rft.subject=Language&rft.subject=Dynamical+Systems&rft.subject=Semantics&rft.subject=Syntax&rft.subject=Logic&rft.description=At+the+end+of+the+19th+century%2C+'logic'+moved+from+the+discipline+of+philosophy+to+that+of+mathematics.+One+hundred+years+later%2C+we+have+a+plethora+of+formal+logics.+Looking+at+the+situation+form+informatics%2C+the+mathematical+discipline+proved+only+a+temporary+shelter+for+%60logic'.+For+there+is+Domain+Theory%2C+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++%60universals'%2C+that+is%2C+model+independent+operands+and+operators.+With+these+universals%2C+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%2C+Aristotelian+(categorical)+logic.+This+is+no+accident.++For+Aristotle%2C+deduction+was+type-dependent+and+he+too+thought+in+term+of+type+independent+universal+%60essences'.+This+paper+initiates+the+next+%60logical'+step+%60beyond'+Domain+Theory++by+reconnecting+%60formal+logic'+with+its+origin.&rft.date=2010-09-02&rft.type=Preprint&rft.type=NonPeerReviewed&rft.format=application%2Fpdf&rft.identifier=http%3A%2F%2Fcogprints.org%2F6948%2F1%2FSmallCalculus.pdf&rft.identifier=++Brillowski%2C+Dr.+Claus++(2010)+From+Domains+Towards+a+Logic+of+Universals%3A+A+Small+Calculus+for+the+Continuous+Determination+of+Worlds.++%5BPreprint%5D+++++&rft.relation=http%3A%2F%2Fcogprints.org%2F6948%2F