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Tense operators on \(m\)-symmetric algebras. (English) Zbl 1256.03068
Summary: Here we initiate an investigation of the equational classes of \(m\)-symmetric algebras endowed with two tense operators. These varieties are a generalization of tense algebras. Our main interest is the duality theory for these classes of algebras. In order to do this, we require Urquart’s duality for Ockham algebras and Goldblatt’s duality for bounded distributive lattice with operations. The dualities enable us to describe the lattices of congruences on tense \(m\)-symmetric algebras.

MSC:
03G25 Other algebras related to logic
03B44 Temporal logic
06D50 Lattices and duality
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