2000 character limit reached
The higher dimensional propositional calculus (2204.00435v4)
Published 1 Apr 2022 in cs.LO
Abstract: In recent research, some of the present authors introduced the concept of an n-dimensional Boolean algebra and its corresponding propositional logic nCL, generalising the Boolean propositional calculus to n>= 2 perfectly symmetric truth values. This paper presents a sound and complete sequent calculus for nCL, named nLK. We provide two proofs of completeness: one syntactic and one semantic. The former implies as a corollary that nLK enjoys the cut admissibility property. The latter relies on the generalisation to the n-ary case of the classical proof based on the Lindenbaum algebra of formulas and Boolean ultrafilters.