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, 15:28, 17 December 2008→1.3.4.14. Application of OF : Generic Level: HTML --> TeX
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:
{| 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>
|}
|}