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If the number of propositions that are being joined together is finite, then the conjunction and the surjunction can be represented by means of sentential connectives, incorporating the sentences that represent these propositions into finite strings of symbols.

If the number of propositions that are being joined together is finite, then the conjunction and the surjunction can be represented by means of sentential connectives, incorporating the sentences that represent these propositions into finite strings of symbols.

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If <math>J\!</math> is finite, for instance, if <math>J\!</math> consists of the integers in the interval <math>j = 1 ~\text{to}~ k,</math> and if each proposition <math>q_j\!</math> is represented by a sentence <math>s_j,\!</math> then the following strategies of expression are open:

If J is finite, for instance, if J constitutes the interval j = 1 to k,

 

and if each proposition Q_j is represented by a sentence S_j, then the

following strategies of expression are open:

 

1.  The conjunction Conj^J_j Q_j can be represented by a sentence that

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

    Conj^J_j Q_j  <-<   S_1 S_2 ... S_k.

<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>

2.  The surjunction Surj^J_j Q_j can be represented by a sentence that

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

    Surj^J_j Q_j  <-<  -(S_1, S_2, ..., S_k)-.

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If one opts for a mode of interpretation that moves more directly from

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:

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

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

node denotes, its logical denotation or its logical interpretation.

node denotes, its logical denotation or its logical interpretation.