Abstract
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.
This work was partly supported by the German Research Council (DFG) as part of the Transregional Collaborative Research Center “Automatic Verification and Analysis of Complex Systems” (SFB/TR 14 AVACS). See www.avacs.org for more information.
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Sofronie-Stokkermans, V. (2005). Hierarchic Reasoning in Local Theory Extensions. In: Nieuwenhuis, R. (eds) Automated Deduction – CADE-20. CADE 2005. Lecture Notes in Computer Science(), vol 3632. Springer, Berlin, Heidelberg. https://doi.org/10.1007/11532231_16
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DOI: https://doi.org/10.1007/11532231_16
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