An alternative notion of quantifiers on three-valued Łukasiewicz algebras
The notion of an existential m-quantifier on a three-valued Łukasiewicz algebra is introduced and studied. The class of three-valued Łukasiewicz algebras endowed with an existential m-quantifier is equational and hence determines a variety denoted by Vm. We prove that the existential m-quantifiers a...
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2017
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| Acceso en línea: | https://bibliotecadigital.exactas.uba.ar/collection/paper/document/paper_15423980_v28_n4-5_p335_Petrovich http://hdl.handle.net/20.500.12110/paper_15423980_v28_n4-5_p335_Petrovich |
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| Sumario: | The notion of an existential m-quantifier on a three-valued Łukasiewicz algebra is introduced and studied. The class of three-valued Łukasiewicz algebras endowed with an existential m-quantifier is equational and hence determines a variety denoted by Vm. We prove that the existential m-quantifiers are interdefinable with the existential quantifiers introduced by Luiz Monteiro. Hence every algebra in Vm is term equivalent to a monadic three-valued Łok;ukasiewicz algebra. We characterize the simple algebras in the variety Vm which turns out to be semisimple. We also find some connections between existential mquantifiers and those existential quantifiers defined on bounded distributive lattices considered by Cignoli in [3], including Boolean algebras. Finally, we prove a Kripke-style representation theorem. ©2017 Old City Publishing, Inc. |
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