ua nt - p h / 99 12 06 5 v 1 1 3 D ec 1 99 9 About the Notion of Truth in the Decoherent Histories Approach : a Reply to Griffiths

Griffiths claims that the “single family rule”, a basic postulate of the decoherent histories approach, rules out our requirement that any decoherent history has a unique truth value, independently from the decoherent family to which it may belong. Here we analyze the reasons which make our requirement indispensable and we discuss the consequences of rejecting it. This short letter is a reply to Griffiths’ article Consistent histories, quantum truth functionals, and hidden variables [1], in which he has raised some objections to our paper Can the decoherent histories description of reality be considered satisfactory? [2]. For a more detailed analysis of the arguments of [2], we refer the reader to [3]. First of all, we would like to summarize the main features of the DH approach, about which there seems not to be a disagreement between Griffiths and us: 1. Within a given decoherent family everything goes like in Classical Mechanics: the probability distribution assigned to the histories obeys the classical probability rules; it is possible to define a Boolean structure, so it is possible to speak about the conjunction, disjunction of two histories and about the negation of an history; moreover, one can define the logical implication between two histories, so that also reasonings of the type “if ... then ...” are possible. e-mail: [email protected] e-mail: [email protected]