On compositional semantics

We prove a theorem stating that any semantics can be encoded as a composit ional semantics, which means that, essentially, the standard definition of composit ionali ty is formally vacuous. We then show that when one requires composi t ional semantics to be "systematic" ( that is the meaning funct ion cannot be arbitrary, but mus t belong to some class), one can easily distinguish between composit ional and non-composi t ional semantics. We also present an example o f a simple g rammar for which there is no "systematic" composit ional semantics. This implies that it is possible to distinguish "good" and "bad" grammars oll the basis of whether they can have composit ional semantics. As a result, we believe that the paper clarifies the concept o f compositionali ty and opens a possibility of making systematic compar isons o f different systems of grammars and N L U programs.