Changes

<p>The conjunction <math>\operatorname{Conj}_j^J q_j</math> can be represented by a sentence that is constructed by concatenating the <math>s_j\!</math> in the following fashion:</p>

<p>The conjunction <math>\operatorname{Conj}_j^J q_j</math> can be represented by a sentence that is constructed by concatenating the <math>s_j\!</math> in the following fashion:</p>

<p><math>\operatorname{Conj}_j^J q_j ~\leftarrowtail~ s_1 s_2 \ldots s_k.</math></p></li>

<p><math>\operatorname{Conj}_j^J q_j ~\leftrightsquigarrow~ s_1 s_2 \ldots s_k.</math></p></li>

<li>

<li>

<p>The surjunction <math>\operatorname{Surj}_j^J q_j</math> can be represented by a sentence that is constructed by surcatenating the <math>s_j\!</math> in the following fashion:</p>

<p>The surjunction <math>\operatorname{Surj}_j^J q_j</math> can be represented by a sentence that is constructed by surcatenating the <math>s_j\!</math> in the following fashion:</p>

<p><math>\operatorname{Surj}_j^J q_j ~\leftarrowtail~ \underline{(} s_1, s_2, \ldots, s_k \underline{)}.</math></p></li>

<p><math>\operatorname{Surj}_j^J q_j ~\leftrightsquigarrow~ \underline{(} s_1, s_2, \ldots, s_k \underline{)}.</math></p></li>

</ol>

</ol>

If one opts for a mode of interpretation that moves more directly from the parse graph of a sentence to the potential logical meaning of both the PARC and the PARCE, then the following specifications are in order:

If one opts for a mode of interpretation that moves more directly from the parse graph of a sentence to the potential logical meaning of both the PARC and the PARCE, then the following specifications are in order:

A cactus rooted at a particular node is taken to represent what that node denotes, its logical denotation or its logical interpretation.

A cactus rooted at a particular node is taken to represent what that

node denotes, its logical denotation or its logical interpretation.

1.  The logical denotation of a node is the logical conjunction of that node's

# The logical denotation of a node is the logical conjunction of that node's arguments, which are defined as the logical denotations of that node's attachments.  The logical denotation of either a blank symbol or an empty node is the boolean value <math>\underline{1} = \operatorname{true}.</math> The logical denotation of the paint <math>\mathfrak{p}_j\!</math> is the proposition <math>p_j,\!</math> a proposition that is regarded as ''primitive'', at least, with respect to the level of analysis that is represented in the current instance of <math>\mathfrak{C} (\mathfrak{P}).</math>

    "arguments", which are defined as the logical denotations of that node's

# The logical denotation of a lobe is the logical surjunction of that lobe's arguments, which are defined as the logical denotations of that lobe's accoutrements.  As a corollary, the logical denotation of the parse graph of <math>\underline{(} \underline{)},</math> otherwise called a ''needle'', is the boolean value <math>\underline{0} = \operatorname{false}.</math>

    attachments.  The logical denotation of either a blank symbol or an empty

    node is the boolean value %1% = "true".  The logical denotation of the

    paint p_j is the proposition P_j, a proposition that is regarded as

    "primitive", at least, with respect to the level of analysis that

    is represented in the current instance of !C!(!P!).

 

2.  The logical denotation of a lobe is the logical surjunction of that lobe's

    "arguments", which are defined as the logical denotations of that lobe's

    accoutrements.  As a corollary, the logical denotation of the parse graph

    of "-()-", otherwise called a "needle", is the boolean value %0% = "false".

If one takes the point of view that PARC's and PARCE's amount to a

If one takes the point of view that PARC's and PARCE's amount to a

pair of intertranslatable languages for the same domain of objects,

pair of intertranslatable languages for the same domain of objects,