On Hierarchical Reasoning in Combinations of Theories

Ihlemann, Carsten; Sofronie-Stokkermans, Viorica

doi:10.1007/978-3-642-14203-1_4

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On Hierarchical Reasoning in Combinations of Theories

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Ihlemann, Carsten
Automation of Logic, MPI for Informatics, Max Planck Society;

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Sofronie-Stokkermans, Viorica
Automation of Logic, MPI for Informatics, Max Planck Society;

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Citation

Ihlemann, C., & Sofronie-Stokkermans, V. (2010). On Hierarchical Reasoning in Combinations of Theories. In J. Giesl, & R. Hähnle (Eds.), Automated Reasoning (pp. 30-45). Berlin: Springer. doi:10.1007/978-3-642-14203-1_4.

Cite as: https://hdl.handle.net/11858/00-001M-0000-000F-14B9-D

Abstract

In this paper we study theory combinations over non-disjoint signatures in which hierarchical and modular reasoning is possible. We use a notion of locality of a theory extension parameterized by a closure operator on ground terms. We give criteria for recognizing these types of theory extensions. We then show that combinations of extensions of theories which are local in this extended sense also have a locality property and hence allow modular and hierarchical reasoning. We thus obtain parameterized decidability and complexity results for many (combinations of) theories important in verification.