Abstract.
Product logic Π is an important t-norm based fuzzy logic with conjunction interpreted as multiplication on the real unit interval [0,1], while Cancellative hoop logic CHL is a related logic with connectives interpreted as for Π but on the real unit interval with 0 removed (0,1]. Here we present several analytic proof systems for Π and CHL, including hypersequent calculi, co-NP labelled calculi and sequent calculi.
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Metcalfe, G., Olivetti, N. & Gabbay, D. Analytic Calculi for Product Logics. Arch. Math. Logic 43, 859–889 (2004). https://doi.org/10.1007/s00153-004-0225-3
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DOI: https://doi.org/10.1007/s00153-004-0225-3