Coinductive Uniform Proofs

03/18/2019

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by   Ekaterina Komendantskaya, et al.

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Coinduction occurs in two guises in Horn clause logic: in proofs of circular properties and relations, and in proofs involving construction of infinite data. Both instances of coinductive reasoning appeared in the literature before, but a systematic analysis of these two kinds of proofs and of their relation was lacking. We propose a general proof-theoretic framework for handling both kinds of coinduction arising in Horn clause logic. To this aim, we propose a coinductive extension of Miller et al framework of uniform proofs and prove its soundness relative to coinductive models of Horn clause logic.