Squares of opposition: Comparisons between syllogistic and propositional logic.
Colwyn Williamson · Notre Dame Journal of Formal Logic · 1972
It has been pointed out, for example by Bocheήski, 1 that the principles of propositional logic now known as DeMorgan's Laws bear a certain resemblance to the laws depicted in the traditional Square of Opposition.The analogy, however, is not as perfect as it could be.The aim of this paper is to explore some of the consequences of seeking a more exact comparison between syllogistic and propositional logic.The propositional operator K (conjunction) may be defined as follows: if 11 = 1, #10 = 0, #01 = 0, #00 = 0. We may therefore regard the resulting values, 1000, as a satisfactory definition of K. Eight further operators will be defined in the same way: B= 1101