An Alternative Definition of Quantifiers on Four-Valued ?ukasiewicz Algebras

摘要

AbstractAn alternative notion of an existential quantifier on four-valued ?ukasiewicz algebras is introduced. The class of four-valued ?ukasiewicz algebras endowed with this existential quantifier determines a variety which is denoted by$$mathbb {M}_{rac{2}{3}}mathbb {L}_4$$M23L4. It is shown that the alternative existential quantifier is interdefinable with the standard existential quantifier on a four-valued ?ukasiewicz algebra. Some connections between the new existential quantifier and the existential quantifiers defined on bounded distributive lattices and Boolean algebras are given. Finally, a completeness theorem for the monadic four-valued ?ukasiewicz predicate calculus corresponding to the dual of the alternative existential quantifier is proven.]]>