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Directory:Jon Awbrey/Papers/Cactus Language (view source)
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, 17:29, 9 January 2009→The Cactus Language : Stylistics: markup
\end{matrix}</math>
\end{matrix}</math>
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It is useful to examine the relationship between the grammatical covering or production relation <math>(:>\!)</math> and the logical relation of implication <math>(\Rightarrow),</math> with one eye to what they have in common and one eye to how they differ. The production <math>q :> W\!</math> says that the appearance of the symbol <math>q\!</math> in a sentential form implies the possibility of exchanging it for <math>W.\!</math> Although this sounds like a ''possible implication'', to the extent that ''<math>q\!</math> implies a possible <math>W\!</math>'' or that ''<math>q\!</math> possibly implies <math>W,\!</math>'' the qualifiers ''possible'' and ''possibly'' are the critical elements in these statements, and they are crucial to the meaning of what is actually being implied. In effect, these qualifications reverse the direction of implication, yielding <math>^{\backprime\backprime} \, q \Leftarrow W \, ^{\prime\prime}</math> as the best analogue for the sense of the production.
<pre>
<pre>
One way to sum this up is to say that non-terminal symbols have the
One way to sum this up is to say that non-terminal symbols have the
significance of hypotheses. The terminal strings form the empirical
significance of hypotheses. The terminal strings form the empirical