Transitive Closure Logic: Infinitary and Cyclic Proof Systems

Authors: Reuben Rowe and Liron Cohen

Paper Information

Title:Transitive Closure Logic: Infinitary and Cyclic Proof Systems
Authors:Reuben Rowe and Liron Cohen
Proceedings:PARIS Contributed papers
Editors: Alexis Saurin, David Baelde and Radu Calinescu
Keywords:Transitive Closure, Induction, Infinitary Proofs, Cyclic Proofs

ABSTRACT. Transitive closure logic is a known extension of first-order logic obtained by introducing a transitive closure operator. While other extensions of first-order logic with inductive definitions are a priori parametrized by a set of inductive definitions, the addition of the transitive closure operator uniformly captures all finitary inductive definitions. We present an infinitary proof system for transitive closure logic which is an infinite descent-style counterpart to the existing (explicit induction) proof system for the logic. We show that, as for similar systems for first-order logic with inductive definitions, our infinitary system is complete for the standard semantics and subsumes the explicit system. Moreover, the uniformity of the transitive closure operator allows semantically meaningful complete restrictions to be defined using simple syntactic criteria.

Talk:Jul 08 16:00 (Session 42M: Contributed talks)