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  1. Analytic Calculi for Product Logics.George Metcalfe, Nicola Olivetti & Dov Gabbay - 2004 - Archive for Mathematical Logic 43 (7):859-889.
    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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  • Group Representation for Even and Odd Involutive Commutative Residuated Chains.Sándor Jenei - 2022 - Studia Logica 110 (4):881-922.
    For odd and for even involutive, commutative residuated chains a representation theorem is presented in this paper by means of direct systems of abelian o-groups equipped with further structure. This generalizes the corresponding result of J. M. Dunnabout finite Sugihara monoids.
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  • Involutive Uninorm Logic with Fixed Point enjoys finite strong standard completeness.Sándor Jenei - 2022 - Archive for Mathematical Logic 62 (1):67-86.
    An algebraic proof is presented for the finite strong standard completeness of the Involutive Uninorm Logic with Fixed Point ($${{\mathbf {IUL}}^{fp}}$$ IUL fp ). It may provide a first step towards settling the standard completeness problem for the Involutive Uninorm Logic ($${\mathbf {IUL}}$$ IUL, posed in G. Metcalfe, F. Montagna. (J Symb Log 72:834–864, 2007)) in an algebraic manner. The result is proved via an embedding theorem which is based on the structural description of the class of odd involutive FL$$_e$$ (...)
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