Linearity and negation
Kenji Tokuo · Journal of Applied Non-Classical Logics · 2012
The logical structure derived from the algebra of generalised projection operators on a module is investigated. With the assumption of the operators being linear, the associated logic becomes Boolean, while without the assumption, the logic does not admit negation: the concept of linearity of projection operators on a module corresponds to that of negation in Boolean logic. The logic of nonlinear operators is formalised and its soundness and completeness results are proved.