The Extendible Functional Concepts of Logic And Its Applications for the Classical Logic
Feng Qing Zhao · 2021
Firstly, this paper considers a new function, called the Cartesian function. Use the function, a generalized concept of logic is obtained and we call it the Cartesian logic. Secondly, as application, the Cartesian {0,1}-logic is introduced, and the dialectical relations of propositions of Cartesian {0,1}-logic are presented, they are generalizations of the logical square of opposition. Further, the logical operations and independence of propositions with the Cartesian theory of truth are studied. Obviously, Cartesian {0,1}-logic is compatible with classical logic and Boolean algebras. Finally, Liar Paradox and Curry's Paradox with their different versions are discussed.