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• W2108232891 abstract "The term Boolean should be used for describing an object that is to categories what a Boolean algebra is to posets. More speciflcally, 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 of proof nets as a particularly well-behaved example of a Boolean category." @default.
• W2108232891 created "2016-06-24" @default.
• W2108232891 creator A5029941199 @default.
• W2108232891 date "2005-12-22" @default.
• W2108232891 modified "2023-09-27" @default.
• W2108232891 title "On the Axiomatisation of Boolean Categories with and without Medial" @default.
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• W2108232891 hasPublicationYear "2005" @default.
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