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Keywords:
Residuated $\ell $-monoid; deductive system; $\mathit {BL}$-algebra; $\mathit {MV}$-algebra; Heyting algebra; filter
Residuated $\ell $-monoid; deductive system; $\mathit {BL}$-algebra; $\mathit {MV}$-algebra; Heyting algebra; filter
Summary:
Bounded commutative residuated lattice ordered monoids ($R\ell $-monoids) are a common generalization of $\mathit {BL}$-algebras and Heyting algebras, i.e. algebras of basic fuzzy logic and intuitionistic logic, respectively. In the paper we develop the theory of filters of bounded commutative $R\ell $-monoids.
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