swMATH ID: 10406
Software Authors: Claessen, Koen; Lillieström, Ann; Smallbone, Nicholas
Description: Sort it out with monotonicity. Translating between many-sorted and unsorted first-order logic. We present a novel analysis for sorted logic, which determines if a given sort is monotone. The domain of a monotone sort can always be extended with an extra element. We use this analysis to significantly improve well-known translations between unsorted and many-sorted logic, making use of the fact that it is cheaper to translate monotone sorts than non-monotone sorts. Many interesting problems are more naturally expressed in many-sorted first-order logic than in unsorted logic, but most existing highly-efficient automated theorem provers solve problems only in unsorted logic. Conversely, some reasoning tools, for example model finders, can make good use of sort-information in a problem, but most problems today are formulated in unsorted logic. This situation motivates translations in both ways between many-sorted and unsorted problems. We present the monotonicity analysis and its implementation in our tool Monotonox, and also show experimental results on the TPTP benchmark library.
Homepage: http://link.springer.com/chapter/10.1007%2F978-3-642-22438-6_17
Related Software: HOL Light; TPTP; HOL; Kodkod; Isabelle/HOL; ML; Nitpick; Isabelle; SPASS+T; Why3; Hotel Key Card; ETPS; SystemOnTPTP; E Theorem Prover; SmallCheck; QuickCheck; Sledgehammer; Isabelle/jEdit; Isabelle/ZF; z3
Referenced in: 4 Publications

Referenced in 1 Serial

1 Journal of Automated Reasoning

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