Changes

In the present discussion, I am using a particular style of annotation for rule derivations, one that is called ''proof by grammatical paradigm'' or ''proof by syntactic analogy''.  The annotations in the right hand margin of the Rule Box interweave the ''numerators'' and the ''denominators'' of the paradigm being employed, in other words, the alternating terms of comparison in a sequence of analogies.  Taking the syntactic transformations marked in the Rule Box one at a time, each step is licensed by its formal analogy to a previously established rule.

In the present discussion, I am using a particular style of annotation for rule derivations, one that is called ''proof by grammatical paradigm'' or ''proof by syntactic analogy''.  The annotations in the right hand margin of the Rule Box interweave the ''numerators'' and the ''denominators'' of the paradigm being employed, in other words, the alternating terms of comparison in a sequence of analogies.  Taking the syntactic transformations marked in the Rule Box one at a time, each step is licensed by its formal analogy to a previously established rule.

For example, the annnotation <math>X_1 : A_1 :: X_2 : A_2\!</math> may be read to say that <math>X_1\!</math> is to <math>A_1\!</math> as <math>X_2\!</math> is to <math>A_2,\!</math> where the step from <math>A_1\!</math> to <math>A_2\!</math> is permitted by a previously accepted rule.

For example, the annotation <math>X_1 : A_1 :: X_2 : A_2\!</math> may be read to say that <math>X_1\!</math> is to <math>A_1\!</math> as <math>X_2\!</math> is to <math>A_2,\!</math> where the step from <math>A_1\!</math> to <math>A_2\!</math> is permitted by a previously accepted rule.

This can be illustrated by considering the derivation of Rule&nbsp;3 in the augmented form that follows:

This can be illustrated by considering the derivation of Rule&nbsp;3 in the augmented form that follows:

<br>

<br>

As a general rule, the application of a STR involves the recognition of an antecedent condition and the facilitation of a consequent condition.  The antecedent condition is a state whose initial expression presents a match, in a formal sense, to one of the sentences that are listed in the STR, and the consequent condition is achieved by taking its suggestions seriously, in other words, by following its sequence of equivalents and implicants to some other link in its chain.

As a general rule, the application of an STR involves the recognition of an antecedent condition and the facilitation of a consequent condition.  The antecedent condition is a state whose initial expression presents a match, in a formal sense, to one of the sentences that are listed in the STR, and the consequent condition is achieved by taking its suggestions seriously, in other words, by following its sequence of equivalents and implicants to some other link in its chain.

Generally speaking, the application of a rule involves the recognition of an antecedent condition as a case that falls under a clause of the rule.  This means that the antecedent condition is able to be captured in the form, conceived in the guise, expressed in the manner, grasped in the pattern, or recognized in the shape of one of the sentences in a list of equivalents or a chain of implicants.

Generally speaking, the application of a rule involves the recognition of an antecedent condition as a case that falls under a clause of the rule.  This means that the antecedent condition is able to be captured in the form, conceived in the guise, expressed in the manner, grasped in the pattern, or recognized in the shape of one of the sentences in a list of equivalents or a chain of implicants.