Basic hoops: an algebraic study of continuous t-norms

DOI10.1007/s11225-007-9078-1zbMath1127.03049OpenAlexW1972451186MaRDI QIDQ2462673

I. M. A. Ferreirim, Paolo Agliano, Franco Montagna

Publication date: 3 December 2007

Published in: Studia Logica (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s11225-007-9078-1

zbMATH Keywords

basic hoops subreducts of BL-algebras

Mathematics Subject Classification ID

Other algebras related to logic (03G25) Ordered semigroups and monoids (06F05)

Related Items

HOOPS WITH QUASI-VALUATION MAPS ⋮ Nodal filters in hoop algebras ⋮ Franco Montagna's work on provability logic and many-valued logic ⋮ On n ‐contractive fuzzy logics ⋮ Construction of some algebras of logics by using intuitionistic fuzzy filters on hoops ⋮ Hoop twist-structures ⋮ The variety generated by all the ordinal sums of perfect MV-chains ⋮ Multipotent GBL-algebras ⋮ Falling Shadow Theory with Applications in Hoops ⋮ Unnamed Item ⋮ The geometry of discrete \(L\)-algebras ⋮ Varieties of K-lattices ⋮ Varieties of bounded K-lattices ⋮ Ordinal sums: from triangular norms to bi- and multivariate copulas ⋮ Mathematical Fuzzy Logics ⋮ Fragments of quasi-Nelson: residuation ⋮ Structural and universal completeness in algebra and logic ⋮ Completeness with respect to a chain and universal models in fuzzy logic ⋮ Results on Hyper Hoop-Algebras ⋮ On some questions concerning the axiomatisation of WNM-algebras and their subvarieties ⋮ Indecomposability of free algebras in some subvarieties of residuated lattices and their bounded subreducts ⋮ Amalgamation property for some varieties of BL-algebras generated by one finite set of BL-chains with finitely many components ⋮ Obituary: Franco Montagna (1948--2015) ⋮ Complexity of some language fragments of fuzzy logics ⋮ Varieties of BL-algebras. I, revisited ⋮ Constructing a Hoop Using Rough Filters ⋮ States and internal states on semihoops ⋮ Amalgamation property for varieties of BL-algebras generated by one chain with finitely many components ⋮ \(\Delta\)-core fuzzy logics with propositional quantifiers, quantifier elimination and uniform Craig interpolation ⋮ Unnamed Item ⋮ Introduction ⋮ Unnamed Item ⋮ State hoops ⋮ Rotation logics ⋮ Fuzzy regular relation on hyper hoop-algebras ⋮ Varieties generated by standard BL-algebras ⋮ Finite model property and varieties of BL-algebras ⋮ State maps on semihoops ⋮ \(n\)-contractive BL-logics ⋮ On the predicate logics of continuous t-norm BL-algebras ⋮ Generalized continuous and left-continuous t-norms arising from algebraic semantics for fuzzy logics ⋮ Fuzzy logics from substructural perspective ⋮ Logic for abstract hoop twist-structures ⋮ Varieties of BL-algebras. III: Splitting algebras ⋮ Varieties of BL-algebras. II ⋮ Monadic bounded hoops ⋮ Results on equality algebras ⋮ On the Equational Characterization of Continuous t-Norms ⋮ Algebras of Fuzzy Sets in Logics Based on Continuous Triangular Norms ⋮ On linear varieties of MTL-algebras ⋮ First-order t-norm based fuzzy logics with truth-constants: distinguished semantics and completeness properties ⋮ A temporal semantics for basic logic ⋮ A short note on divisible residuated semilattices ⋮ Splittings in subreducts of hoops ⋮ Splittings in GBL-algebras. I: The general case ⋮ Splittings in GBL-algebras. II: The representable case ⋮ Mathematical fuzzy logic as a tool for the treatment of vague information ⋮ Projectivity in (bounded) commutative integral residuated lattices ⋮ A categorical equivalence for product algebras ⋮ Varieties of BL-algebras ⋮ Generating the variety of BL-algebras

Cites Work