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 …

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

The subject of this thesis is the proof theory of logics with fixed points, such as the μ-
calculus, linear-logic with fixed points, etc. These logics are usually equipped with finitary …

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 introduce a path-based cyclic proof system for first-order-calculus, the extension of first-
order logic by second-order quantifiers for least and greatest fixed points of definable …

Abstract Automata operating on infinite objects feature prominently in the theory of the modal-
calculus. One such application concerns the tableau games introduced by Niwiński & …

We investigate non-wellfounded proof systems based on parsimonious logic, a weaker
variant of linear logic where the exponential modality! is interpreted as a constructor for …

Cyclic proof systems, in which induction is managed implicitly, are a promising approach to
automatic verification. The soundness of cyclic proof graphs is ensured by checking them …

Cyclic proof systems permit derivations that are finite graphs in contrast to conventional
derivation trees. The soundness of such proofs is ensured by a condition on the paths …

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 …