Standardized notation can be helpful, especially after a topic has matured. For example, Gentzen used as an infix symbol to build sequents from lists of formulas. While one also sees used, it seems that in recent years, has become the standard, especially when proof theory is applied to type theory (where is invariably used) and…
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Brouwer meets Kripke: constructivising modal logic
Intuitionistic logic and modal logic each admit meaningful projections of classical theories. While intuitionistic logic can interpret classical logic by a host of translations, thus yielding computational interpretations, modal logic can be employed to understand notions of provability and truth. However, the enrichment of intuitionistic logic by modalities is far less canonical than its classical…
LK vs LJ: An origin story for linear logic
In his 1987 TCS paper [2], Girard credits semantic considerations related to coherent models as the origin of the key observation behind linear logic: the intuitionistic implication should be split into two connectives . To the extent that it makes sense to propose an alternative origin story for linear logic, it is interesting to note…
Confluence in the sequent calculus
In this blog post, we give an insight into the confluence of the sequent calculus, a property mainly considered since the discovery of the so-called Curry-Howard correspondence [1]. Confluence is often thought to be part of the well-understood folklore. For people already aware of the links between intuitionism and computation, it may feel natural and…
