A Resolution Calculus for Presuppositions
Autor: Manfred Kerber and Michael Kohlhase
Herausgeber: Wolfgang Wahlster
The semantics of everyday language and the semantics of
its naive translation into classical first-order 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
non-empty, while in classical logic it is only assumed that the
whole universe is non-empty. 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 many-valued logics were developed to model these
phenomena much better than classical first-order logic can do. An
adequate calculus, however, has not yet been given. Recent years
have seen a thorough investigation of the framework of many-valued
truth-functional logics. Unfortunately, restricted quantifications
are not truth-functional, hence they do not fit the framework
directly. We solve this problem by applying recent methods from
sorted logics.
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