We describe the design and implementation of an automated theorem prover realising a
fully general notion of cyclic proof. Our tool, called Cyclist, is able to construct proofs obeying …

Infinitary and regular proofs are commonly used in fixed point logics. Being natural
intermediate devices between semantics and traditional finitary proof systems, they are …

This paper establishes cut-elimination for, and, that are non-wellfounded sequent calculi
with least and greatest fixed-points, by expanding on prior works by Santocanale and Fortier …

Cyclic proof provides a style of proof for logics with inductive (and coinductive) definitions, in
which proofs are cyclic graphs representing a form of argument by infinite descent. It is …

We present two finitary cut-free sequent calculi for the modal μ-calculus. One is a variant of
Kozen's axiomatisation in which cut is replaced by a strengthening of the induction rule for …

Given that (co) inductive types are naturally modelled as fixed points, it is unsurprising that
fixed-point logics are of interest in the study of programming languages, via the Curry …

One of the authors introduced in [Santocanale, FoSSaCS, 2002] a calculus of circular proofs
for studying the computability arising from the following categorical operations: finite …

We present a general automated proof procedure, based upon cyclic proof, for inductive
entailments in separation logic. Our procedure has been implemented via a deep …

We describe the first approach to automatically synthesizing heap-manipulating programs
with auxiliary recursive procedures. Such procedures occur routinely in data structure …

We introduce a sound non-wellfounded proof system whose regular (or 'cyclic') proofs are
complete for (in) equations between regular expressions. We achieve regularity by using …