A tense algebra is a structure A = (A,∨,0,
∧,1,¬,◊f, ◊p) such that both
(A,∨,0,∧,1,¬,◊f) and (A,∨,0,∧,1,¬,◊p) are modal algebras,and
◊p and ◊f are conjugates: x∧◊py = 0 iff ◊fx∧y = 0
Remark: Tense algebras provide algebraic models for logic of tenses. The two possibility operators ◊p and ◊f are intuitively interpreted as at some past instance and at some future instance.
Let A and B be tense algebras. A morphism from A to B is a function h : A → B that is a Boolean homomorphism and preserves ◊p and ◊f: h(◊x) = ◊h(x).
|Congruence n-permutable||yes, n = 2|
|Congruence extension property||yes|
|Definable principal congruences||no|
|Equationally definable principal congruences||no|
|Strong amalgamation property||yes|
|Epimorphisms are surjective||yes|