11  Interpretation in SL

The interpretation of a sentence or set of sentences in SL involves an assignment of a truth value to all non-logical symbols in it. The non-logical symbols in SL include upper-case letters only. All other symbols are logical.

Thus, in SL, the \(i\) (interpretation) function involves assigning a truth value to every non-logical symbol \(\pi\) in a set of sentences.1 Suppose \(\Pi\) is the set of such symbols. Then:

\[i : \Pi \to \{1,0\}\]

that is, \(i\) maps every \(\pi\) to a truth value, 1 or 0. In application, then:

\[i: \pi \mapsto 1 \quad \text{or} \quad i: \pi \mapsto 0\]

That is, an interpretation makes each \(\pi\) true or false.

  1. As a reminder, the only non-logical symbols in SL are upper-case letters, so in practice \(\pi\) will be \(A, B,\) or \(C,\) etc.↩︎