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What could a Boolean category be?

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 should be 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 talk I will sketch a series (with increasing strength) of possible such axiomatisations, all based on the notion of *-autonomous category. There will be some 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.
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Contributor : Lutz Straßburger <>
Submitted on : Monday, February 12, 2007 - 3:51:11 PM
Last modification on : Thursday, January 7, 2021 - 3:40:14 PM
Long-term archiving on: : Tuesday, April 6, 2010 - 9:29:26 PM


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  • HAL Id : inria-00130504, version 1



Lutz Straßburger. What could a Boolean category be?. Classical Logic and Computation 2006 (ICALP Workshop), Jul 2006, Venice, Italy. ⟨inria-00130504⟩



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