A Resolution Calculus for Presuppositions
Author: Manfred Kerber and Michael Kohlhase
Editor: Wolfgang Wahlster
The semantics of everyday language and the semantics of
its naive translation into classical firstorder language
considerably differ. An important discrepancy that is addressed in
this paper is about the implicit assumption what exists. For
instance, in the case of universal quantification natural language
uses restrictions and presupposes that these restrictions are
nonempty, while in classical logic it is only assumed that the
whole universe is nonempty. On the other hand, all constants
mentioned in classical logic are presupposed to exist, while it
makes no problems to speak about hypothetical objects in everyday
language. These problems have been discussed in philosophical logic
and some adequate manyvalued logics were developed to model these
phenomena much better than classical firstorder logic can do. An
adequate calculus, however, has not yet been given. Recent years
have seen a thorough investigation of the framework of manyvalued
truthfunctional logics. Unfortunately, restricted quantifications
are not truthfunctional, hence they do not fit the framework
directly. We solve this problem by applying recent methods from
sorted logics.
