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Directory:Jon Awbrey/Papers/Syntactic Transformations (view source)
Revision as of 19:52, 9 February 2009
, 19:52, 9 February 2009→Derived Equivalence Relations: format definition box
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{| align="center" cellpadding="0" cellspacing="0" style="border-left:1px solid black; border-top:1px solid black; border-right:1px solid black; border-bottom:1px solid black" width="90%"
Definition 11
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{| align="center" cellpadding="0" cellspacing="0" width="100%"
If R c OxSxI,
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then the following are identical subsets of SxO:
| width="20%" | <math>\operatorname{Definition~11}</math>
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D11a. RSO
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D11b. ROS^
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D11c. DenR^
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| width="18%" style="border-top:1px solid black" | <math>\text{If}\!</math>
D11d. Den(R)^
| width="80%" style="border-top:1px solid black" | <math>L ~\subseteq~ O \times S \times I</math>
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D11e. PrSO(R)
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| <math>\text{then}\!</math>
D11f. Conv(Den(R))
| <math>\text{the following are identical subsets of}~ S \times O \, :</math>
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D11g. {<s, o> C SxO : <o, s, i> C R for some i C I}
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{| align="center" cellpadding="0" cellspacing="0" width="100%"
|- style="height:50px"
| width="2%" style="border-top:1px solid black" |
| width="18%" style="border-top:1px solid black" | <math>\operatorname{D11a.}</math>
| width="80%" style="border-top:1px solid black" | <math>L_{SO}\!</math>
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| <math>\operatorname{D11b.}</math>
| <math>\overset{\smile}{L_{OS}}</math>
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| <math>\operatorname{D11c.}</math>
| <math>\overset{\smile}{\operatorname{Den}^L}</math>
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| <math>\operatorname{D11d.}</math>
| <math>\overset{\smile}{\operatorname{Den}(L)}</math>
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| <math>\operatorname{D11e.}</math>
| <math>\operatorname{proj}_{SO}(L)</math>
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| <math>\operatorname{D11f.}</math>
| <math>\operatorname{Conv}(\operatorname{Den}(L))</math>
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| <math>\operatorname{D11g.}</math>
| <math>\{ (s, o) \in S \times O ~:~ (o, s, i) \in L ~\operatorname{for~some}~ i \in I \}</math>
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