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Monotonicity Inference for Higher-Order Formulas

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Abstract

Formulas are often monotonic in the sense that satisfiability for a given domain of discourse entails satisfiability for all larger domains. Monotonicity is undecidable in general, but we devised three calculi that infer it in many cases for higher-order logic. The third calculus has been implemented in Isabelle’s model finder Nitpick, where it is used both to prune the search space and to soundly interpret infinite types with finite sets, leading to dramatic speed and precision improvements.

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Authors and Affiliations

  1. Institut für Informatik, Technische Universität München, Munich, Germany

    Jasmin Christian Blanchette & Alexander Krauss

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  1. Jasmin Christian Blanchette
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  2. Alexander Krauss
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Correspondence to Jasmin Christian Blanchette.

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Research partially supported by the Deutsche Forschungsgemeinschaft (grants Ni 491/11-1 and Ni 491/11-2).

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Blanchette, J.C., Krauss, A. Monotonicity Inference for Higher-Order Formulas. J Autom Reasoning 47, 369–398 (2011). https://doi.org/10.1007/s10817-011-9234-1

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