 To handle partially defined truth predicates, it is necessary to introduce the notion of partial models. In a partial model for a first-order language, each \(n\)-place predicate symbol \(P\) is interpreted by a pair \((U,V)\) of disjoint \(n\)-place relations on the domain of the model. \(U\) is called the extension of \(P\) and \(V\) its anti-extension. In the model, \(P\) is true of the objects in \(U\), false of the objects in \(V\), and undefined otherwise. In this way, any atomic sentence receives one of the truth values true, false or undefined in the model. Non-atomic formulae are given truth values in the model by using Kleene’s strong three-valued logic for evaluating the connectives. 