Logical connectives | Ternary operations

Conditioned disjunction

In logic, conditioned disjunction (sometimes called conditional disjunction) is a ternary logical connective introduced by Church. Given operands p, q, and r, which represent truth-valued propositions, the meaning of the conditioned disjunction [p, q, r] is given by: In words, [p, q, r] is equivalent to: "if q then p, else r", or "p or r, according as q or not q". This may also be stated as "q implies p, and not q implies r". So, for any values of p, q, and r, the value of [p, q, r] is the value of p when q is true, and is the value of r otherwise. The conditioned disjunction is also equivalent to: and has the same truth table as the ternary conditional operator ?: in many programming languages. In electronic logic terms, it may also be viewed as a single-bit multiplexer. In conjunction with truth constants denoting each truth-value, conditioned disjunction is for classical logic. Its truth table is the following: There are other truth-functionally complete ternary connectives. (Wikipedia).

Conditioned disjunction
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Related pages

Ternary operation | Logical connective | Truth table | Proposition | Alonzo Church | Ternary conditional operator | Classical logic