Conditioned disjunction
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In logic, conditioned disjunction is a ternary operator that, in conjunction with a truth constant denoting each truth-value, is truth-functionally complete . It is typically written [p,q,r] and read "p or r, according as q or not q". For any values of p, q, r, [p,q,r] receives the value of p when q is true, and it receives the value of r otherwise. Its truth table is the following:
| p | q | r | [p,q,r] |
|---|---|---|---|
| T | T | T | T |
| T | T | F | T |
| T | F | T | T |
| T | F | F | F |
| F | T | T | F |
| F | T | F | F |
| F | F | T | T |
| F | F | F | F |
There are other truth-functionally complete ternary connectives. See, e.g., Wesselkamper T., A sole sufficient operator, Notre Dame Journal of Formal Logic, Vol. XVI, No. 1 (1975), pp. 86-88.
