Doğrudan indirgemeler üzerine iki değerli mantık açısından bir inceleme - II: Aynı basit önermelerden oluşturulan bileşik önermelerin birbirine indirgenmesi

Abstract

The joint denial proposition “it is neither true that the sea is foggy nor that it is not foggy” and the incompatibility proposition “it is not true that the sea is both foggy and not foggy”; the disjunction proposition “the student is diligent or not diligent” and the conjunction proposition “it is not true that the student is diligent and not diligent”; the incompatibility proposition “it is not true that the city of Paris is both within the borders of the country of France and not within the borders of the country of France” and the conjunction proposition “it is not true that the city of Paris is within the borders of the country of France and not within the borders of the country of France” are compound propositions created from the same simple propositions and reducible to each other in the context of two-valued logic. Like these propositions, many compound propositions created from the same simple propositions can be reduced to each other. In this study, it is tried to reveal all the variations of reducing compound propositions created from the same simple propositions to each other in the context of two-valued logic. In the first part of the study, the reduction of the compound propositions with the same simple propositions formed without the use of negation joints is included. In the second part, the reduction of compound propositions with the same simple propositions created using the negation joint is included. In the third part, compound propositions with the same simple proposition formed without using the negation joint and compound propositions with the same simple proposition formed using the negation joint, which are reduced to each other, are included.