Abstract

Hodges' Extension Theorem is perfectly designed for the kind of extension problem of principle of compositionality, which arises in the so-called IF languages. These languages satisfy the conditions of the application of the Extension Theorem. They are extensions of standard first-order languages closed under atomic and negations of atomic formulas and disjunctions and conjunctions of IF-formulas. Hodges' extension theorem shows that when certain conditions are satisfied, a language has a unique compositional interpretation, which agrees with the initially given partial one. Accordingly, any two such compositional interpretations must be formally equivalent. Kaplan separates the indices, which contribute to the semantic value of a sentence into those that make the context of utterance, and those that constitute the circumstances of evaluation. The former determine what is said and the latter determine whether what is said is true or false.