Besides their use as natural proof systems for various fixpoint logics, non-wellfounded proofs have also been studied from the perpective of the Curry-Howard correspondence of proofs as programs, both for intuitionistic and linear logic. In recent work with Afshari and Leigh, I have studied the comptutational content of non-wellfounded proofs for classical logic via so-called Herbrand schemes.
In this talk I will present current work in progress where I explore a different approach, adapting Parigot's lambda-mu-calculus to the setting of non-wellfounded proofs.
I will present the system along with some background and discussion of computational intepretations of classical logic in general. I will also say a few things about problems on which I am working at the moment, in particular confluence and normalization of the calculus. Uniform interpolation is a strong form of Craig interpolation, which says that propositional quantifiers can be interpreted inside the logic.
Uniform interpolants can be constructed via a proof-theoretic method which was first proposed by Pitts The event is inspired by the departmental logic seminars that are organized at each university, and aims to unify the universities for a collaborative seminar. Besides hosting a main speaker, the seminar will also be the location of the award ceremony of the VvL MSc Thesis Prize winners, who will give a short presentation of their thesis.
Details, including speakers, abstract and information about registration, can be found on the event website. There are three key ideas. First, a syntactic formula loading mechanism is used to identify repeats caused by the star operator, similar to the focus mechanism in other cyclic proof systems. Second, a syntactic mechanism is used to eliminate repeats that arise from unguarded formulas. However, interpolants obtained via the modal mu-calculus are not guaranteed to belong to the PDL fragment.
