February 1954
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2,628 Citations
The Mathematical Gazette
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... The involution-free reduct of i-ubands coincides with the variety of unital bands (i.e., idempotent monoids), whose subvariety lattice is characterized in [27] (see also [11]). Interestingly, and aside from their obvious generalization of Boolean algebras and classical propositional logic, i-ubands are general enough to provide a common root for a large class of other well-studied algebras related to nonclassical logics, such as ortho(modular) lattices (related to the foundation of quantum logic), De Morgan algebras (related to mathematical fuzzy logic), and in particular also for Kleene 3-valued logics (see [15,6]), showing that the logic of McCarthy can be seen as their non-commutative companion (see also [12]). ...
- Citing Article
February 1954
The Mathematical Gazette