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Efficient hierarchical reasoning about functions over numerical domains

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

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Sofronie-Stokkermans, V. (2008). Efficient hierarchical reasoning about functions over numerical domains. In A. R. Dengel, K. Berns, T. M. Breuel, F. Bomarius, & T. R. Roth-Berghofer (Eds.), KI 2008: Advances in Artificial Intelligence: 31st Annual German Conference on AI, KI 2008 (pp. 135-143). Berlin: Springer.


Cite as: http://hdl.handle.net/11858/00-001M-0000-000F-1B79-3
Abstract
We show that many properties studied in mathematical analysis (e.g.\ monotonicity, boundedness, inverse or Lipschitz properties, possibly combined with continuity and/or derivability) are expressible as axioms in a class for which sound and complete hierarchical proof methods for testing satisfiability of ground formulae exist. The results are useful for automated reasoning in analysis, and in the verification of hybrid systems.