Displaying similar documents to “Priestley dualities for some lattice-ordered algebraic structures, including MTL, IMTL and MV-algebras”

Preserving Filtering Unification by Adding Compatible Operations to Some Heyting Algebras

Wojciech Dzik, Sándor Radeleczki (2016)

Bulletin of the Section of Logic

Similarity:

We show that adding compatible operations to Heyting algebras and to commutative residuated lattices, both satisfying the Stone law ¬x ⋁ ¬¬x = 1, preserves filtering (or directed) unification, that is, the property that for every two unifiers there is a unifier more general then both of them. Contrary to that, often adding new operations to algebras results in changing the unification type. To prove the results we apply the theorems of [9] on direct products of l-algebras and filtering...

Some properties of residuated lattices

Radim Bělohlávek (2003)

Czechoslovak Mathematical Journal

Similarity:

We investigate some (universal algebraic) properties of residuated lattices—algebras which play the role of structures of truth values of various systems of fuzzy logic.

Conjugated algebras

Ivan Chajda (2009)

Acta Universitatis Palackianae Olomucensis. Facultas Rerum Naturalium. Mathematica

Similarity:

We generalize the correspondence between basic algebras and lattices with section antitone involutions to a more general case where no lattice properties are assumed. These algebras are called conjugated if this correspondence is one-to-one. We get conditions for the conjugary of such algebras and introduce the induced relation. Necessary and sufficient conditions are given to indicated when the induced relation is a quasiorder which has “nice properties", e.g. the unary operations are...