Affiliation:
1. Ege University, Faculty of Sciences, Department of Mathematics, Izmir, Turkey
Abstract
In this paper, we analyze the algebraic properties of categorical syllogisms
by constructing a logical calculus system called Syllogistic Logic with
Carroll Diagrams (SLCD).We prove that any categorical syllogism is valid if
and only if it is provable in this system. For this purpose, we explain
firstly the quantitative relation between two terms by means of bilateral
diagrams and we clarify premises via bilateral diagrams. Afterwards, we
input the data taken from bilateral diagrams, on the trilateral diagram.
With the help of the elimination method, we obtain a conclusion that is
transformed from trilateral diagram to bilateral diagram. Subsequently, we
study a syllogistic conclusion mapping which gives us a conclusion obtained
from premises. Finally, we allege valid forms of syllogisms using algebraic
methods, and we examine their algebraic properties, and also by using
syllogisms, we construct algebraic structures, such as lattices, Boolean
algebras, Boolean rings, and many-valued algebras (MV-algebras).
Publisher
National Library of Serbia
Cited by
2 articles.
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