An Algebraic Analysis of Categorical Syllogisms by Using Carroll's Diagrams
Küçük Resim Yok
Tarih
2019
Yazarlar
Dergi Başlığı
Dergi ISSN
Cilt Başlığı
Yayıncı
Univ Nis, Fac Sci Math
Erişim Hakkı
info:eu-repo/semantics/openAccess
Özet
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).
Açıklama
Anahtar Kelimeler
Categorical syllogisms, completeness, validity, algebraic logic
Kaynak
Filomat
WoS Q Değeri
Q2
Scopus Q Değeri
Cilt
33
Sayı
2
