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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 negated
Note 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.
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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 |