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Directory:Jon Awbrey/Papers/Cactus Language (view source)
Revision as of 19:58, 6 January 2009
, 19:58, 6 January 2009→Grammar 4: markup
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If this is beginning to sound like a monotone condition, then it is not absurd to sharpen the resemblance and render the likeness more acute. This is done by declaring a couple of ordering relations, denoting them under variant interpretations by the same sign, <math>^{\backprime\backprime}\!< \, ^{\prime\prime}.</math>
If this is beginning to sound like a monotone condition, then it is
not absurd to sharpen the resemblance and render the likeness more
# The ordering <math>^{\backprime\backprime}\!< \, ^{\prime\prime}</math> on the set of non-terminal symbols, <math>q \in \{ \, ^{\backprime\backprime} \, S \, ^{\prime\prime} \, \} \cup \mathfrak{Q},</math> ordains the initial symbol <math>^{\backprime\backprime} \, S \, ^{\prime\prime}</math> to be strictly prior to every intermediate symbol. This is tantamount to the axiom that <math>^{\backprime\backprime} \, S \, ^{\prime\prime} < q,</math> for all <math>q \in \mathfrak{Q}.</math>
acute. This is done by declaring a couple of ordering relations,
# The ordering <math>^{\backprime\backprime}\!< \, ^{\prime\prime}</math> on the collection of sentential forms, <math>W \in \{ \, ^{\backprime\backprime} \, S \, ^{\prime\prime} \, \} \cup (\mathfrak{Q} \cup \mathfrak{A})^*,</math> ordains the empty string to be strictly minor to every other sentential form. This is stipulated in the axiom that <math>\varepsilon < W,</math> for every non-empty sentential form <math>W.\!</math>
denoting them under variant interpretations by the same sign "<".
Given these two orderings, the constraint in question on intermediate significance can be stated as follows:
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{| align="center" cellpadding="12" cellspacing="0" style="border-top:1px solid black" width="90%"
| align="center" style="border-left:1px solid black; border-right:1px solid black" |
<math>\text{Condition On Intermediate Significance}\!</math>
|-
| style="border-top:1px solid black; border-bottom:1px solid black; border-left:1px solid black; border-right:1px solid black" |
<math>\begin{array}{lccc}
\text{If}
& q
& :>
& W
\\
\text{and}
& q
& >
& ^{\backprime\backprime} \, S \, ^{\prime\prime}
\\
\text{then}
& W
& >
& \varepsilon
\\
\end{array}</math>
|}
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Achieving a grammar that respects this convention typically requires a more
Achieving a grammar that respects this convention typically requires a more detailed account of the initial setting of a type, both with regard to the type of context that incites its appearance and also with respect to the minimal strings that arise under the type in question. In order to find covering productions that satisfy the intermediate significance condition, one must be prepared to consider a wider variety of calling contexts or inciting situations that can be noted to surround each recognized type, and also to enumerate a larger number of the smallest cases that can be observed to fall under each significant type.
detailed account of the initial setting of a type, both with regard to the
type of context that incites its appearance and also with respect to the
minimal strings that arise under the type in question. In order to find
covering productions that satisfy the intermediate significance condition,
one must be prepared to consider a wider variety of calling contexts or
inciting situations that can be noted to surround each recognized type,
and also to enumerate a larger number of the smallest cases that can
be observed to fall under each significant type.
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With the array of foregoing considerations in mind,
With the array of foregoing considerations in mind,
one is gradually led to a grammar for !L! = !C!(!P!)
one is gradually led to a grammar for !L! = !C!(!P!)