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A formalization of diagrammatic proofs in abstract rewriting

Abstract

Diagrams are in common use in the rewriting community. In this paper, we present a formalization of this kind of diagrams. We give a formal definition for the diagrams used to state properties. We propose inference rules to formalize the reasoning depicted by some well known diagrammatic proofs : a transitivity property of some abstract rewriting systems and the Newman's lemma. We show that the system proposed is both correct and complete for a class of formulas called coherent logic.
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Dates and versions

inria-00180065 , version 1 (17-10-2007)

Identifiers

  • HAL Id : inria-00180065 , version 1

Cite

Julien Narboux. A formalization of diagrammatic proofs in abstract rewriting. 2006. ⟨inria-00180065⟩
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