  Similarly as classical propositional calculus is based algebraically on
Boolean algebras, the logic of quantum mechanics was based on orthomodular
lattices by G. Birkhoff and J. von Neumann and K. Husimi. However, this logic
does not incorporate time dimension although it is apparent that the
propositions occurring in the logic of quantum mechanics are depending on time.
The aim of the present paper is to show that so-called tense operators can be
introduced also in such a logic for given time set and given time preference
relation. In this case we can introduce these operators in a purely algebraic
way. We derive several important properties of such operators, in particular we
show that they form dynamic pairs and, altogether, a dynamic algebra. We
investigate connections of these operators with logical connectives conjunction
and implication derived from Sasaki projections. Then we solve the converse
problem, namely to find for given time set and given tense operators a time
preference relation in order that the resulting time frame induces the given
operators. We show that the given operators can be obtained as restrictions of
operators induced by a suitable extended time frame.
