Puzzle corner

Puzzle corner: our guest is logic theorist Vincent Danos

“The main concern of this paper is the design of a noetherian and confluent normalization for LK2 (that is, classical second order predicate logic presented as a sequent calculus). The method we present is powerful: since it allows us to recover as fragments formalisms as seemingly different as Girard's LC and Parigot's A.u, FD ([10, 12, 32, 36]), delineates other viable systems as well, and gives means to extend the Krivine/Leivant paradigm of 'programming-with-proofs' ([26, 27]) to classical logic; it is painless: since we reduce strong normalization and confluence to the same properties for linear logic (for non-additive proof nets, to be precise) using appropriate embeddings (so-called decorations); it is unifying: it organizes known solutions in a simple pattern that makes apparent the how and why of their making. A comparison of our method to that of embedding LK into LJ (intuitionistic sequent calculus) brings to the fore the latter's defects for these 'deconstructive purposes'.”

This is from the gripping paper “A new deconstructive logic: linear logic”, which hasn’t received the attention it deserves in the thirteen years since it was first published in the Journal of Symbolic Logic.

Last week’s winner: congratulations to Ytterbium Pancake, who interpreted Mr Kolb’s writings for us: “there are two different types of time: linear time and cyclical time. We’re all familiar with linear time, which is commonly abbreviated as ‘time’. However, the less recognised type of time, cyclical time, is just as important. The best way to visualise it is as a cow falling from a unicycle face-first into a collection of mid-range vacuum cleaners. The vacuum cleaners represent the Bee Gees in chronological order of birth, and the cow represents a teapot the exact size and shape of Ukraine’s Saint Sophia Cathedral.