2018/09/13 by Ekaterina Komendantskaya Dr, Yue Li
Computer Science · #cs.AI #cs.LO
paper · pdf · doi:10.4204/eptcs.278.5
published as EPTCS 278, 2018, pp. 27-33 · In Proceedings HCVS 2018, arXiv:1809.04554
arxiv created 2018/09/13 · arxiv updated 2018/09/14
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.