Skip to Main content Skip to Navigation
Other publications

On the Axiomatisation of Boolean Categories with and without Medial

Lutz Straßburger 1, 2
1 PARSIFAL - Proof search and reasoning with logic specifications
LIX - Laboratoire d'informatique de l'École polytechnique [Palaiseau], Inria Saclay - Ile de France
Abstract : In its most general meaning, a Boolean category is to categories what a Boolean algebra is to posets. In a more specific meaning a Boolean category should provide the abstract algebraic structure underlying the proofs in Boolean Logic, in the same sense as a Cartesian closed category captures the proofs in intuitionistic logic and a *-autonomous category captures the proofs in linear logic. However, recent work has shown that there is no canonical axiomatisation of a Boolean category. In this work, we will see a series (with increasing strength) of possible such axiomatisations, all based on the notion of *-autonomous category. We will particularly focus on the medial map, which has its origin in an inference rule in KS, a cut-free deductive system for Boolean logic in the calculus of structures. Finally, we will present a category proof nets as a particularly well-behaved example of a Boolean category.
Complete list of metadata

Cited literature [45 references]  Display  Hide  Download
Contributor : Lutz Straßburger <>
Submitted on : Monday, February 12, 2007 - 3:44:51 PM
Last modification on : Thursday, January 7, 2021 - 3:40:14 PM
Long-term archiving on: : Tuesday, April 6, 2010 - 9:42:28 PM


Files produced by the author(s)


  • HAL Id : inria-00130508, version 1



Lutz Straßburger. On the Axiomatisation of Boolean Categories with and without Medial. 2006. ⟨inria-00130508⟩



Record views


Files downloads