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Reviving Basic Narrowing Modulo

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Frontiers of Combining Systems (FroCoS 2019)

Part of the book series: Lecture Notes in Computer Science ((LNAI,volume 11715))

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Abstract

We define an inference rule called the Parallel rule. Given a rewrite system R and an equational theory E, where R is E-convergent modulo, we show that if R is saturated under the Parallel rule then Basic Narrowing modulo E is complete for R. If R is finitely saturated under both Parallel and Forward Overlap then Basic Narrowing, with right hand side abstracted, is complete and terminates, and thus it is a decision procedure for unification modulo \(R \cup E\). We give examples, such as the theory of XOR, the theory of abelian groups and Associativity with a unit element. We also show that R has the finite variant property modulo E if and only if R can be finitely saturated under Parallel and Forward Overlap, provided that E unification is finitary.

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Correspondence to Christopher Lynch .

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Kim, D., Lynch, C., Narendran, P. (2019). Reviving Basic Narrowing Modulo. In: Herzig, A., Popescu, A. (eds) Frontiers of Combining Systems. FroCoS 2019. Lecture Notes in Computer Science(), vol 11715. Springer, Cham. https://doi.org/10.1007/978-3-030-29007-8_18

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  • DOI: https://doi.org/10.1007/978-3-030-29007-8_18

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  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-030-29006-1

  • Online ISBN: 978-3-030-29007-8

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