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General E-unification with Eager Variable Elimination and a Nice Cycle Rule

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Abstract

We present a goal-directed E-unification procedure with eager Variable Elimination and a new rule, Cycle, for the case of collapsing equations – that is, equations of the type x ≈ v where x ∈Var(v). Cycle replaces Variable Decomposition (or the so-called Root Imitation) and thus removes possibility of some obviously unnecessary infinite paths of inferences in the E-unification procedure. We prove that, as in other approaches, such inferences into variable positions in our goal-directed procedure are not needed. Our system is independent of selection rule and complete for any E-unification problem.

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  1. Theoretical Computer Science, Dresden University of Technology, 01062, Dresden, Germany

    Barbara Morawska

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  1. Barbara Morawska
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Correspondence to Barbara Morawska.

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Morawska, B. General E-unification with Eager Variable Elimination and a Nice Cycle Rule. J Autom Reasoning 39, 77–106 (2007). https://doi.org/10.1007/s10817-007-9068-z

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