A Boolean algebra for a formal expression of events in logical systems

The dynamic modelling of logical systems widely calls upon the event notion. In terms of Function Chart Grafcet or Petri Nets for instance, events are generally represented by "rising or falling edges" of logical variables. However, numerous ambiguities are encountered in the models because the translation of events into edges is not formal enough. In this paper, we propose a Boolean algebra the definition-set of which allows us to describe the time behavior of the inputs and the outputs of any logical system. In this algebra, we have defined two unary operations in order to formally express the events. Then, we are giving 14 properties related to these rising and falling edge operations and their composition with the operations AND, OR, and NOT.