LBPC-I paraconsistent system (2006)
The language of the LBPc¬I system extends the language of positive classical logic by including a weak negation operator and an incompatibility operator, in addition, it allows defining a strong negation operator; The latter has all the characteristics of classical negation. The system is characterized by a semantics of traditional valuations with which it is proved that, with respect to the weak negation operator, the system is paraconsistent. As expected, when the formulas involved in an argument behave classically, that is, they are incompatible with their weak denial, then weak denial behaves like classical denial, but this requirement is not always necessary, weak denial can be punctually as powerful as the classic one, although the formulas involved do not behave classically.