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Properties of Constrained Generalization Algorithms

14 pagesPublished: October 19, 2017


Two non deterministic algorithms for generalizing a solution of a constraint expressed in second order typed lambda-calculus are presented. One algorithm derives from the proof of completeness of the higher order unification rules by D. C. Jensen and T. Pietrzykowski, the other is abstracted from an algorithm by N. Peltier and the author for generalizing proofs. A framework is developed in which such constrained generalization algorithms can be designed, allowing a uniform presentation for the two algorithms. Their relative strength at generalization is then analyzed through some properties of interest: their behaviour on valid and first order constraints, or whether they may be iterated or composed.

Keyphrases: generalization, second-order constraints, typed lambda calculus

In: Christoph Benzmüller, Christine Lisetti and Martin Theobald (editors). GCAI 2017. 3rd Global Conference on Artificial Intelligence, vol 50, pages 64--77

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