  Effect algebras were introduced in order to describe the structure of
effects, i.e. events in quantum mechanics. They are partial algebras describing
the logic behind the corresponding events. It is natural to ask how to
introduce the logical connective implication in effect algebras. For
lattice-ordered effect algebras this task was already solved by several
authors, including the present ones. We concentrate on effect algebras that
need not be lattice-ordered since these can better describe the events
occurring in the quantum physical system. Although an effect algebra is only
partial, we try to find a logical connective implication which is everywhere
defined. But such a connective can be "unsharp" or "inexact" because its
outputs for given pairs of entries need not be elements of the underlying
effect algebra, but may be subsets of (mutually incomparable) maximal elements.
We introduce such an implication together with its adjoint functor representing
conjunction. Then we consider so-called tense operators on effect algebras. Of
course, also these operators turn out to be "unsharp" in the aforementioned
sense, but they are in a certain relation with the operators implication and
conjunction. Finally, for given tense operators and given time set T, we
describe two methods how to construct a time preference relation R on T such
that the given tense operators are either comparable with or equivalent to
those induced by the time frame (T,R).
