The main result in this paper is a method for obtaining derivation trees from sentences of certain formal grammars. No parsing algorithm was previously known to exist for these grammars.Applied to Montague's PTQ the method produces all parses that could correspond to different meanings. The technique directly addresses scope and reference and provides a framework for examining these phenomena. The solution for PTQ is implemented in an efficient and useful computer program.

Many people have noted the similarities between case theories in linguistics and frame representations in artificial intelligence. In particular, the cases of a verb seem to correspond to the slots of a frame. This has led many people, including Fillmore [1977] and Winston [1977] to assert that cases and slots are one and the same. This hypothesis has not attracted much attention, probably because the notion of “slot” in frame representations is so underconstrained that the theory would seem to be (...) content free. In this note, we wish to show that this is not true. For one thing, the case‐slot identity theory can explain the difficulty linguists have had in deciding how many cases there are. Furthermore, its adoption will place certain interesting, and plausible constraints on the frame and case theories compatible with it. (shrink)