Reasoning in Quantum Theory: Modus Ponens and the co-event interpretation

Classical logic does not apply in quantum theory. However one would like to be able to reason according to some standard rules for quantum systems as well (whether they are an electron or the universe itself). We examine what exactly is needed in order to be able to construct deductive arguments and in particular to maintain the "Modus Ponens" which is the basic deductive rule of inference. It turns out that this requirement restricts the possible theories and in the context of the coevent interpretation it results uniquely to the "multiplicative-scheme".