  Effect algebras form a formal algebraic description of the structure of the
so-called effects in a Hilbert space which serves as an event-state space for
effects in quantum mechanics. This is why effect algebras are considered as
logics of quantum mechanics, more precisely as an algebraic semantics of these
logics. Because every productive logic is is equipped with a connective
implication, we introduce here such a concept and demonstrate its properties.
In particular, we show that this implication is connected with conjunction via
a certain "unsharp" residuation which is formulated on the basis of a strict
unsharp residuated poset. Though this structure is rather complicated, it can
be converted back into an effect algebra and hence it is sound. Further, we
study the Modus Ponens rule for this implication by means of so-called
deductive systems and finally we study the contraposition law.
