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  1. On triangular norm based axiomatic extensions of the weak nilpotent minimum logic.Carles Noguera, Francesc Esteva & Joan Gispert - 2008 - Mathematical Logic Quarterly 54 (4):387-409.
    In this paper we carry out an algebraic investigation of the weak nilpotent minimum logic and its t-norm based axiomatic extensions. We consider the algebraic counterpart of WNM, the variety of WNM-algebras and prove that it is locally finite, so all its subvarieties are generated by finite chains. We give criteria to compare varieties generated by finite families of WNM-chains, in particular varieties generated by standard WNM-chains, or equivalently t-norm based axiomatic extensions of WNM, and we study their standard completeness (...)
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  • On the reflection invariance of residuated chains.Sándor Jenei - 2010 - Annals of Pure and Applied Logic 161 (2):220-227.
    It is shown that, under certain conditions, a subset of the graph of a commutative residuated chain is invariant under a geometric reflection. This result implies that a certain part of the graph of the monoidal operation of a commutative residuated chain determines another part of the graph via the reflection on one hand, and tells us about the structure of continuity points of the monoidal operation on the other. Finally, these results are applied for the subdomains of uniqueness problem, (...)
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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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  • Axiomatic Extensions of IMT3 Logic.Joan Gispert & Antoni Torrens - 2005 - Studia Logica 81 (3):311-324.
    In this paper we characterize, classify and axiomatize all axiomatic extensions of the IMT3 logic. This logic is the axiomatic extension of the involutive monoidal t-norm logic given by ¬φ3 ∨ φ. For our purpose we study the lattice of all subvarieties of the class IMT3, which is the variety of IMTL-algebras given by the equation ¬(x 3) ∨ x ≈ ⊤, and it is the algebraic counterpart of IMT3 logic. Since every subvariety of IMT3 is generated by their totally (...)
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  • Free Algebras in Varieties of Glivenko MTL-Algebras Satisfying the Equation 2(x²) = (2x)².Roberto Cignoli & Antoni Torrens Torrell - 2006 - Studia Logica 83 (1-3):157 - 181.
    The aim of this paper is to give a description of the free algebras in some varieties of Glivenko MTL-algebras having the Boolean retraction property. This description is given (generalizing the results of [9]) in terms of weak Boolean products over Cantor spaces. We prove that in some cases the stalks can be obtained in a constructive way from free kernel DL-algebras, which are the maximal radical of directly indecomposable Glivenko MTL-algebras satisfying the equation in the title. We include examples (...)
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  • Free Algebras in Varieties of Glivenko MTL-algebras Satisfying the Equation 2(x2) = (2x)2.Roberto Cignoli & Antoni Torrens Torrell - 2006 - Studia Logica 83 (1-3):157-181.
    The aim of this paper is to give a description of the free algebras in some varieties of Glivenko MTL-algebras having the Boolean retraction property. This description is given (generalizing the results of [9]) in terms of weak Boolean products over Cantor spaces. We prove that in some cases the stalks can be obtained in a constructive way from free kernel DL-algebras, which are the maximal radical of directly indecomposable Glivenko MTL-algebras satisfying the equation in the title. We include examples (...)
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  • Free nilpotent minimum algebras.Manuela Busaniche - 2006 - Mathematical Logic Quarterly 52 (3):219-236.
    In the present paper we give a description of the free algebra over an arbitrary set of generators in the variety of nilpotent minimum algebras. Such description is given in terms of a weak Boolean product of directly indecomposable algebras over the Boolean space corresponding to the Boolean subalgebra of the free NM-algebra.
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  • The Variety Generated by all the Ordinal Sums of Perfect MV-Chains.Matteo Bianchi - 2013 - Studia Logica 101 (1):11-29.
    We present the logic BLChang, an axiomatic extension of BL (see [23]) whose corresponding algebras form the smallest variety containing all the ordinal sums of perfect MV-chains. We will analyze this logic and the corresponding algebraic semantics in the propositional and in the first-order case. As we will see, moreover, the variety of BLChang-algebras will be strictly connected to the one generated by Chang’s MV-algebra (that is, the variety generated by all the perfect MV-algebras): we will also give some new (...)
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