Connectives and Operators of PL
In PL we use upper case letters (e.g. "A", "B", "C") to symbolize or abbreviate simple propositions, and we use the following symbols to abbreviate the five operators:
| operator | symbol | symbol name |
| not | ~ | tilde |
| and | & | ampersand |
| or | v | wedge |
| if then | ⊃ | horseshoe |
| if and only if | ≡ | triple-bar |
In addition, we will use parentheses whenever our propositions include a binary operator. Parentheses serve as grouping indicators. Here are some examples of symbolizations of English sentences, arrived at through a series of steps:
| sentence: | commentary: |
| Ignat will ski and Fred will go swimming. | Sentence to be translated |
| A and B | where A abbreviates "Ignat will ski." and B abbreviates "Fred will go swimming." |
| (A & B) | Full translation. |
Notice that while we used "A" and "B" to abbreviate the simple sentences, we could have used any upper case letters. It is often useful to use a letter found in the sentence itself. Thus we might have used "I" for the first sentence and "F" for the second. It's your choice!
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