I believe that the validity of [the Fregean principle of compositionality] is beyond doubt and thus any grammar, whether organized to reflect [it] directly or not, may ultimately be required to satisfy it. One of the systems that are precisely designed to reflect [it] is Montague Grammar, where, technical details aside, it is realized as follows: (2) a. Sentences are composed by putting their constituents together step by step, with no subsequent rearrangement; b. Not only each lexical item but also (...) each rule of composition is assigned an explicit interpretation; c. Interpretation is given in terms of model theory: the denotation conditions of expressions are defined relative to a mathematical construct which, loosely speaking, models the relevant aspects of the world talked about. (shrink)