12 found
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  1.  35
    A Proof of Standard Completeness for Esteva and Godo's Logic MTL.Sándor Jenei & Franco Montagna - 2002 - Studia Logica 70 (2):183-192.
    In the present paper we show that any at most countable linearly-ordered commutative residuated lattice can be embedded into a commutative residuated lattice on the real unit interval [0, 1]. We use this result to show that Esteva and Godo''s logic MTL is complete with respect to interpretations into commutative residuated lattices on [0, 1]. This solves an open problem raised in.
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  2.  9
    On the Structure of Rotation-Invariant Semigroups.Sándor Jenei - 2003 - Archive for Mathematical Logic 42 (5):489-514.
    We generalize the notions of Girard algebras and MV-algebras by introducing rotation-invariant semigroups. Based on a geometrical characterization, we present five construction methods which result in rotation-invariant semigroups and in particular, Girard algebras and MV-algebras. We characterize divisibility of MV-algebras, and point out that integrality of Girard algebras follows from their other axioms.
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  3.  5
    Equality Algebras.Sándor Jenei - 2012 - Studia Logica 100 (6):1201-1209.
    A new structure, called equality algebras, will be introduced. It has two connectives, a meet operation and an equivalence, and a constant. A closure operator will be defined in the class of equality algebras, and we call the closed algebras equivalential. We show that equivalential equality algebras are term equivalent with BCK-algebras with meet. As a by-product, we obtain a quite general result, which is analogous to a result of Kabziński and Wroński: we provide an equational characterization for the equivalential (...)
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  4.  17
    Pseudo Equality Algebras.Sándor Jenei & László Kóródi - 2013 - Archive for Mathematical Logic 52 (5-6):469-481.
    A new structure, called pseudo equality algebras, will be introduced. It has a constant and three connectives: a meet operation and two equivalences. A closure operator will be introduced in the class of pseudo equality algebras; we call the closed algebras equivalential. We show that equivalential pseudo equality algebras are term equivalent with pseudo BCK-meet-semilattices. As a by-product we obtain a general result, which is analogous to a result of Kabziński and Wroński: we provide an equational characterization for the equivalence (...)
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  5.  22
    Erratum to “On the Reflection Invariance of Residuated Chains” [Ann. Pure Appl. Logic 161 220–227].Sándor Jenei - 2010 - Annals of Pure and Applied Logic 161 (12):1603-1604.
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  6.  3
    On the Reflection Invariance of Residuated Chains.Sándor Jenei - 2009 - 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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  7.  22
    On Involutive FL E -Monoids.Sándor Jenei & Hiroakira Ono - 2012 - Archive for Mathematical Logic 51 (7-8):719-738.
    The paper deals with involutive FL e -monoids, that is, commutative residuated, partially-ordered monoids with an involutive negation. Involutive FL e -monoids over lattices are exactly involutive FL e -algebras, the algebraic counterparts of the substructural logic IUL. A cone representation is given for conic involutive FL e -monoids, along with a new construction method, called twin-rotation. Some classes of finite involutive FL e -chains are classified by using the notion of rank of involutive FL e -chains, and a kind (...)
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  8. Mathematical Logic.Sandor Jenei - 2003 - Archive for Mathematical Logic 42:489.
     
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  9.  11
    Structure of Left-Continuous Triangular Norms with Strong Induced Negations Rotation-Annihilation Construction.Sándor Jenei - 2001 - Journal of Applied Non-Classical Logics 11 (3-4):351-366.
    This paper is the continuation of [11] where the rotation construction of left-continuous triangular norms was presented. Here the class of triangular subnorms and a second construction, called rotation-annihilation, are introduced: Let T1 be a left-continuous triangular norm. If T1 has no zero divisors then let T2 be a left-continuous rotation invariant t-subnorm. If T1 has zero divisors then let T2 be a left-continuous rotation invariant triangular norm. From each such pair the rotation-annihilation construction produces a left-continuous triangular norm with (...)
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  10.  12
    Structure of Left-Continuous Triangular Norms with Strong Induced Negations (I) Rotation Construction.Sándor Jenei - 2000 - Journal of Applied Non-Classical Logics 10 (1):83-92.
    ABSTRACT A new algebraic construction -called rotation- is introduced in this paper which from any left-continuous triangular norm which has no zero divisors produces a left-continuous but not continuous triangular norm with strong induced negation. An infinite number of new families of such triangular norms can be constructed in this way which provides a huge spectrum of choice for e.g. logical and set theoretical connectives in non-classical logic and in fuzzy theory. On the other hand, the introduced construction brings us (...)
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  11.  23
    A Classification of Certain Group-Like FL $$_e$$ E -Chains.Sándor Jenei & Franco Montagna - 2015 - Synthese 192 (7):2095-2121.
    Classification of certain group-like FL $_e$ -chains is given: We define absorbent-continuity of FL $_e$ -algebras, along with the notion of subreal chains, and classify absorbent-continuous, group-like FL $_e$ -algebras over subreal chains: The algebra is determined by its negative cone, and the negative cone can only be chosen from a certain subclass of BL-chains, namely, one with components which are either cancellative (that is, those components are negative cones of totally ordered Abelian groups) or two-element MV-algebras, and with no (...)
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  12.  15
    Erratum To: A Classification of Certain Group-Like FL $$_e$$ E -Chains.Sándor Jenei & Franco Montagna - 2016 - Synthese 193 (1):313-313.
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