MyWikiBiz, Author Your Legacy — Thursday October 31, 2024
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, 15:28, 17 December 2008
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| I recall the objective genre of ''properties and instances'' and re-introduce the symbols <math>\lessdot</math> and <math>\gtrdot</math> for the converse pair of dyadic relations that generate it. Reverting to the convention I employ in formal discussions of applying relational operators on the right, it is convenient to express the relative terms "property of <math>x\!</math>" and "instance of <math>x\!</math>" by means of a case inflection on <math>x\!,</math> that is, as "<math>x\!</math>’s property" and "<math>x\!</math>’s instance", respectively. Described in this way, <math>\operatorname{OG} (\operatorname{Prop}, \operatorname{Inst}) = \langle \lessdot, \gtrdot \rangle,</math> where: | | I recall the objective genre of ''properties and instances'' and re-introduce the symbols <math>\lessdot</math> and <math>\gtrdot</math> for the converse pair of dyadic relations that generate it. Reverting to the convention I employ in formal discussions of applying relational operators on the right, it is convenient to express the relative terms "property of <math>x\!</math>" and "instance of <math>x\!</math>" by means of a case inflection on <math>x\!,</math> that is, as "<math>x\!</math>’s property" and "<math>x\!</math>’s instance", respectively. Described in this way, <math>\operatorname{OG} (\operatorname{Prop}, \operatorname{Inst}) = \langle \lessdot, \gtrdot \rangle,</math> where: |
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− | :{|
| + | {| align="center" cellpadding="8" |
− | | ''x'' <math>\lessdot</math> | + | | <math>x \lessdot</math> |
− | | = | + | | <math>=\!</math> |
− | | ''x''’s Property | + | | <math>x \operatorname{'s~Property}</math> |
− | | = | + | | <math>=\!</math> |
− | | Property of ''x'' | + | | <math>\operatorname{Property~of}\ x </math> |
− | | = | + | | <math>=\!</math> |
− | | Object above ''x'' , | + | | <math>\operatorname{Object~above}\ x,</math> |
| |- | | |- |
− | | ''x'' <math>\gtrdot</math> | + | | <math>x \gtrdot</math> |
− | | = | + | | <math>=\!</math> |
− | | ''x''’s Instance | + | | <math>x \operatorname{'s~Instance}</math> |
− | | = | + | | <math>=\!</math> |
− | | Instance of ''x'' | + | | <math>\operatorname{Instance~of}\ x </math> |
− | | = | + | | <math>=\!</math> |
− | | Object below ''x'' . | + | | <math>\operatorname{Object~below}\ x.</math> |
| |} | | |} |
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