Technical Report MSC-2001-03

TR#:MSC-2001-03
Class:MSC
Title: Base Dependence of Extensions for Open Default Theories
Authors: Julia Mosin (Rubin)
Supervisors: Michael Kaminski
PDFMSC-2001-03.pdf
Abstract: In this thesis we compare the semantic and syntactic definitions of extensions for open default theories. We prove that, over monadic languages, the two definitions are equivalent and do not depend on the cardinality of the underlying infinite world. Thus, for monadic languages, the semantic definition of extensions can always be restricted to a countable base. Next, we present a syntactic definition of extensions for open default theories over a weaker logic. We show that this definition is not equivalent to the definition which was introduced previously. Nevertheless, we prove that it does not depend on the cardinality of the underlying infinite world as well.

Finally, we prove that, for uniterm default theories over finite languages not containing function symbols, the syntactic definition of extensions does not depend on the cardinality of the underlying world. Using this result we show that, in the case of explicitly defined finite domains, the semantic definition of extensions for uniterm default theories over finite languages not containing function symbols can always be restricted to a finite base.

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