Results 61 to 70 of about 2,056 (173)
Hidden modalities in algebras with negation and implication [PDF]
, 2013 Lukasiewicz 3-valued logic may be seen as a logic with hidden truthfunctional modalities de ned by A := :A ! A and A := :(A ! :A). It is known that axioms (K), (T), (B), (D), (S4), (S5) are provable for these modalities, and rule (RN) is admissible. We
Järvinen, Jouni +3 more
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Abstract residuation over lattices [PDF]
Bulletin of the American Mathematical Society, 1938 The idea of residuation goes back to Dedekind [3], † who introduced it in the theory of modules. It has since had extensive applications in the theory of algebraic modular systems [6], in the theory of ideals [8], and in certain topics of arithmetic [9]. On account of its fundamental role in several fields of modern algebra, it is desirable to consider
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Some decompositions of filters in residuated lattices
Analele Stiintifice ale Universitatii Ovidius Constanta: Seria Matematica, 2019 In this paper we introduce a new class of residuated lattice: residuated lattice with (C∧&→) property and we prove that (C∧&→) ⇔ (C→) + (C∧).Also, we introduce and characterize C→, C∨, C∧ and C∧ & → filters in residuated lattices (i.e., we characterize ...
Piciu Dana +2 more
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Quantale Modules and their Operators, with Applications
, 2009 The central topic of this work is the categories of modules over unital quantales. The main categorical properties are established and a special class of operators, called Q-module transforms, is defined.
Russo, Ciro
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A note on drastic product logic [PDF]
, 2014 The drastic product $*_D$ is known to be the smallest $t$-norm, since $x *_D y = 0$ whenever $x, y < 1$. This $t$-norm is not left-continuous, and hence it does not admit a residuum.
B. Schweizer +9 more
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The Structure of Semiconic Idempotent Commutative Residuated Lattices
MathematicsIn this paper, we study semiconic idempotent commutative residuated lattices. After giving some properties of such residuated lattices, we obtain a structure theorem for semiconic idempotent commutative residuated lattices. As an application, we make use
Wei Chen
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Kernels of Residuated Maps as Complete Congruences in Lattices
International Journal of Computational Intelligence Systems, 2020 In a context of lattice-valued functions (also called lattice-valued fuzzy sets), where the codomain is a complete lattice L, an equivalence relation defined on L by the equality of related cuts is investigated.
Branimir Šešelja, Andreja Tepavčević
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Canonical formulas for k-potent commutative, integral, residuated lattices
, 2016 Canonical formulas are a powerful tool for studying intuitionistic and modal logics. Actually, they provide a uniform and semantic way to axiomatise all extensions of intuitionistic logic and all modal logics above K4.
Bezhanishvili, Nick +2 more
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Interval-valued algebras and fuzzy logics [PDF]
, 2010 In this chapter, we present a propositional calculus for several interval-valued fuzzy logics, i.e., logics having intervals as truth values. More precisely, the truth values are preferably subintervals of the unit interval.
Cornelis, Chris +2 more
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Kragujevac Journal of MathematicsThis paper is devoted to the study of a fascinating class of residuated lattices, the so-called mp-residuated lattice, in which any prime filter contains a unique minimal prime filter. A combination of algebraic and topological methods is applied to obtain new and structural results on mp-residuated lattices.
Rasouli, Saeed, Dehghani, Amin
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