A Complete Cyclic Proof System for Inductive Entailments in First Order Logic

19 pages•Published: October 23, 2018

Abstract

In this paper we develop a cyclic proof system for the problem of inclusion between the least sets of models of mutually recursive predicates, when the ground constraints in the inductive definitions are quantifier-free formulae of first order logic. The proof system consists of a small set of inference rules, inspired by a top-down language inclusion algorithm for tree automata [9]. We show the proof system to be sound, in general, and complete, under certain semantic restrictions involving the set of constraints in the inductive system. Moreover, we investigate the computational complexity of checking these restrictions, when the function symbols in the logic are given the canonical Herbrand interpretation.

Keyphrases: antichain-based tree automata language inclusion, cyclic proofs, inductive definitions, infinite descent

In: Gilles Barthe, Geoff Sutcliffe and Margus Veanes (editors). LPAR-22. 22nd International Conference on Logic for Programming, Artificial Intelligence and Reasoning, vol 57, pages 435--453

Links:	https://easychair.org/publications/paper/S1fv
	https://doi.org/10.29007/xgc6