 At each stage in Kripke’s construction, the truth predicate is only partially defined, that is, it only applies to some of the sentences of the language. To deal with such partially defined predicates, a three-valued logic is employed, that is, a logic which operates with a third value, undefined, in addition to the truth values true and false. Often the third value is denoted “\(u\)” or “\(\bot\)” (bottom). A partially defined predicate only receives one of the classical truth values, true or false, when it is applied to one of the terms for which the predicate has been defined, and otherwise it receives the value undefined. There are several different three-valued logics available, differing in how they treat the third value. Here only one of them is briefly described, called Kleene’s strong three-valued logic. More detailed information on this and related logics can be found in the entry on  many-valued logic.