Towards Coinductive Theory Exploration in Horn Clause Logic: Position Paper

09/13/2018

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by   Ekaterina Komendantskaya Dr, et al.

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Coinduction occurs in two guises in Horn clause logic: in proofs of self-referencing properties and relations, and in proofs involving construction of (possibly irregular) 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's framework of uniform proofs and prove its soundness relative to coinductive models of Horn clause logic.