Sequent calculi for induction and infinite descent

@article{Brotherston2011SequentCF,
  title={Sequent calculi for induction and infinite descent},
  author={James Brotherston and Alex K. Simpson},
  journal={J. Log. Comput.},
  year={2011},
  volume={21},
  pages={1177-1216}
}
This paper formalises and compares two different styles of reasoning with inductively defined predicates, each style being encapsulated by a corresponding sequent calculus proof system. The first system, LKID, supports traditional proof by induction, with induction rules formulated as rules for introducing inductively defined predicates on the left of sequents. We show LKID to be cut-free complete with respect to a natural class of Henkin models; the eliminability of cut follows as a corollary… CONTINUE READING
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