In the spring of 1978, one of the authors of this book was sitting in on
a course in logic for linguists given by the other author. In attempting
to present some of Montague's insights in an elementary way (hopefully
avoid- ing the notation which many find difficult at first), the authors
began dis- cussions aimed towards the construction of a simple
model-theoretical semantic apparatus which could be applied directly to
a small English-like language and used to illustrate the methods of
formal logical interpretation. In these discussions two points impressed
themselves on us. First, our task could be simplified by using boolean
algebras and boolean homomorphisms in the models; and second, the
boolean approach we were developing had much more widespread relevance
to the logical structure of English than we first thought. During the
summer and fall of 1978 we continued work on the system, proving the
more fundamental theorems (including what we have come to call the
Justification Theorem) and outlining the way in which an intensional
interpretation scheme could be developed which made use of the boolean
approach (which was originally strictly extensional). We presented our
findings in a monograph (Keenan and Faltz, 1978) which the UCLA
Linguistics Department kindly published as part of their series called
Occa- sional Papers in Linguistics; one of the authors also presented
the system at a colloquium held at the Winter Meeting of the Linguistic
Society of America in December 1978.
