2005 | OriginalPaper | Buchkapitel
Hierarchic Reasoning in Local Theory Extensions
verfasst von : Viorica Sofronie-Stokkermans
Erschienen in: Automated Deduction – CADE-20
Verlag: Springer Berlin Heidelberg
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We show that for special types of extensions of a base theory, which we call
local
, efficient hierarchic reasoning is possible. We identify situations in which it is possible, for an extension
$\mathcal{T}_{1}$
of a theory
$\mathcal{T}_{0}$
, to express the decidability and complexity of the universal theory of
$\mathcal{T}_{1}$
in terms of the decidability resp. complexity of suitable fragments of the theory
$\mathcal{T}_{0}$
(universal or ∀ ∃). These results apply to theories related to data types, but also to certain theories of functions from mathematics.