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 …

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 …

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 …

Matching logic is a logic for specifying and reasoning about structure by means of patterns
and pattern matching. This paper makes two contributions. First, it proposes a sound and …

Verification problems of programs in various paradigms can be reduced to problems of
solving Horn clause constraints on predicate variables that represent unknown inductive …

The symbolic-heap fragment of separation logic has been actively developed and
advocated for verifying the memory-safety property of computer programs. At present, one of …

We study the logical complexity of proofs in cyclic arithmetic (CA), as introduced by Simpson
in [Sim17], in terms of quantifier alternations of formulae occurring. Writing CΣn for (the …

We describe a formal verification framework and tool implementation, based upon cyclic
proofs, for certifying the safe termination of imperative pointer programs with recursive …

A cyclic proof system, called CLKID-omega, gives us another way of representing inductive
definitions and efficient proof search. The 2011 paper by Brotherston and Simpson showed …

We develop a doubly exponential decision procedure for the satisfiability problem of
guarded separation logic—a novel fragment of separation logic featuring user-supplied …