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Directory:Jon Awbrey/Papers/Functional Logic : Inquiry and Analogy (view source)
Revision as of 18:58, 16 November 2009
, 18:58, 16 November 2009→Umpire Operators: use \texttt typeface for logical ops + clarify a bit
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To express it another way:
{| align="center" cellpadding="8" style="text-align:center"
{| align="center" cellpadding="8" style="text-align:center"
| <math>\Upsilon (e, f) = 1\!</math>
| <math>\Upsilon (e, f) = 1\!</math>
| <math>\Leftrightarrow</math>
| <math>\Leftrightarrow</math>
| <math>\underline{(e (f))} = \underline{1}.</math>
| <math>\texttt{(} e \texttt{(} f \texttt{))} = 1</math>
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In writing this, however, it is important to notice that the 1's appearing on the left and right have different meanings. Filling in the details, we have:
In writing this, however, it is important to notice that the <math>1\!</math> appearing on the left side and the <math>1\!</math> appearing on the right side of the logical equivalence have different meanings. Filling in the details, we have:
{| align="center" cellpadding="8" style="text-align:center"
{| align="center" cellpadding="8" style="text-align:center"
| <math>\Upsilon (e, f) = 1 \in \mathbb{B}</math>
| <math>\Upsilon (e, f) = 1 \in \mathbb{B}</math>
| <math>\Leftrightarrow</math>
| <math>\Leftrightarrow</math>
| <math>\underline{(e (f))} = 1 : \langle u, v \rangle \to \mathbb{B}.</math>
| <math>\texttt{(} e \texttt{(} f \texttt{))} = 1 : \langle u, v \rangle \to \mathbb{B}</math>
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