Basic logic with alternating affirmation (2005)
The system language extends the language of classical logic by including an operator for the notion of alternating affirmation (in contrast to the classical affirmation or usual affirmation), and also operators of incompatibility and determinability between the pair of operators denial versus alternate affirmation. The system is characterized by a semantics of valuations, with which the non-equivalence between the two operators is shown. As expected, the system collapses in classical logic if this equivalence is requested. Two intermediate systems are generated when it is requested on the one hand that the alternate statement implies the classical one and on the other hand the reciprocal implication.