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.
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