Where is a set of truth values, a function mapping -tuples in to values in . In semantics with logical matrices, each -ary connective is interpreted by an -ary truth function .
A truth function of a number of propositions or sentences is a function of them that has a definite truth-value, dependent only on the truth-values of the constituents. Thus (p & q) is a combination whose truth-value is true when p is true and q is true, and false otherwise. ¬p is a truth function of p, false when p is true and true when p is false. The way in which the value of the whole is determined by the combinations of values of constituents is presented in a truth table.
The propositional calculus is the standard treatment of truth-functional combinations. Its constants, &, ∨, ¬, → and ↔, are all truth functors, i.e. expressions standing for truth functions.
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