There is an ambiguity to logic, which is concerned with the study of the validity and invalidity of inferences, and to the logical analysis of natural language, which is nowadays a prominent discipline in linguistics and philosophy. An important characteristic of ‘traditional’ logic is that it is truth-functional. In view of the logical analysis of natural languages in which, as in Montague’s approach, a logical language is used in the description of the semantics of natural language, this approach is confronted with severe problems, in the sense that apparently truth-functionality can no longer be upheld. There is, however, also a second set of problems which have to do with what has traditionally been called Frege’s Problem. Gottlob Frege (1848–1925) noticed that an important principle from traditional logic, Leibniz’s law, under certain circumstances did not hold. Any logic which is non-extensional and non-truth-functional is called an intensional logic (as apposed to extensional logic). Examples of intensional logics are modal logic, deontic logic, epistemic logic, temporal logic, as well as the overarching system constructed by Richard Montague for the analysis of natural languages.