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If Wishes Were Horses: The Lojban Connective System
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Lojban regards four of these 16 truth functions as fundamental, and assigns them the four vowels A, E, O, and U. These letters do not represent actual cmavo or selma'o, but rather a component vowel from which actual logical-connective cmavo are built up, as explained in the next section. Here are the four vowels, their truth tables, and rough English equivalents:
A TTTF or, and/or E TFFF and O TFFT if and only if U TTFF whether or not
More precisely:
TTTF A TTFT A with second sentence negated TTFF U TFTT A with first sentence negated TFTF U with sentences exchanged TFFT O TFFF E FTTT A with both sentences negated FTTF O with either first or second negated (not both) FTFT U with sentences exchanged and then second negated FTFF E with second sentence negated FFTT U with first sentence negated FFTF E with first sentence negated FFFT E with both sentences negatedNote that exchanging the sentences is only necessary with U. The three other basic truth functions are commutative; that is, they mean the same thing regardless of the order of the component sentences. There are other ways of getting some of these truth tables; these just happen to be the methods usually employed.
Previous
Logical connection and truth tables |
If Wishes Were Horses: The Lojban Connective System
The Lojban Reference Grammar |
Next
The six types of logical connectives |