Alessio Guglielmi's Research / Sequent Calculus
I list here some recent papers I wrote with my wife about the proof theory of the sequent calculus.
Abstract logic programming is about designing logic programming languages via the proof theoretic notion of uniform provability. It allows the design of purely logical, very expressive logic programming languages, endowed with a rich meta theory. This tutorial intends to expose the main ideas of this discipline in the most direct and simple way.
Full first order linear logic can be presented as an abstract logic programming language in Miller's system Forum, which yields a sensible operational interpretation in the `proof search as computation´ paradigm. However, Forum still has to deal with syntactic details that would normally be ignored by a reasonable operational semantics. In this respect, Forum improves on Gentzen systems for linear logic by restricting the language and the form of inference rules. We further improve on Forum by restricting the class of formulae allowed, in a system we call G-Forum, which is still equivalent to full first order linear logic. The only formulae allowed in G-Forum have the same shape as Forum sequents: the restriction does not diminish expressiveness and makes G-Forum amenable to proof theoretic analysis. G-Forum consists of two (big) inference rules, for which we show a cut elimination procedure. This does not need to appeal to finer detail in formulae and sequents than is provided by G-Forum, thus successfully testing the internal symmetries of our system.