421 218
Full Length Article
Volume 6 , Issue 1, PP: 22-31 , 2020

Title

Classical Logic as a subclass of Neutrosophic Logic

Authors Names :   Angelo de Oliveira   1 *     Marina Nogueira Carvalho de Oliveira   2  

1  Affiliation :  Departamento Academico de Ciencia da Computacao - Universidade Federal de Rondonia, Brasil

    Email :  angelo@unir.br


2  Affiliation :  Undergraduate Student in Civil Engineering, Universidade Tecnologica Federal do Parana, Brasil

    Email :  marina.nogueira.co@gmail.com.br



Doi   :  10.5281/zenodo.3830094


Abstract :

It is customary in mathematics that almost all new developments maintain compatibility with what is already proved and accepted. Following this way, neutrosophic logic has the classical logic as subset. However, in mathematics, all the affirmations must be proved first to be accepted, so the claim that the neutrosophic logic encompass classical logic must be also proved. Thus, this paper show that the main properties of the classical logic hold when translated to neutrosophic form at propositional level.

Keywords :

Neutrosophic Logic; Classical Logic.

References :

[1]  Florentin Smarandache. A Unifying Field in Logics, Neutrosophic Logics: Neutrosophic Logic. Neutros- ophy, Neutrosophic Set, Neutrosophic Probability and Statistics. InfoLearnQuest, 2007. Disponible at: http://fs.unm.edu/eBook-Neutrosophics6.pdf.

[2]  N. C. A da Costa, J. M. Abe, and V. S. Subrahmanian. Remarks on annotated logic. Zeitschrift fur Mathematische Logik und Grundlagen der Mathematik, (37):561–570, 1991.

[3]  Joao Ina´cio da Silva Filho.  Implementac¸a˜o de circuitos lo´gicos fundamentados em uma classe de lo´gicas paraconsistentes anotadas. Master’s thesis, Universidade de Sa˜o Paulo, 1997.

[4]  Joao Ina´cio da Silva Filho.  Me´todos de aplicac¸o˜es da lo´gica paraconsistente anotada de anotac¸a˜o com dois valores-LPA2v com construc¸a˜o de algoritmo e implementac¸a˜o de circuitos eletroˆnicos.  PhD thesis, Universidade de Sa˜o Paulo, 1999.

[5]  Fa´bio Romeu de Carvalho and Jair Minoro Abe. A Paraconsistent Decision-Making Method, volume 87 of

Smart Innovation, Systems and Technologies. Springer, 2018.

[6]  Sheila Souza and Jair Minoro Abe. Paraconsistent Artificial Neural Networks and Aspects of PatternRecognition, volume 94 of Intelligent Systems Reference Library, chapter 9, pages 207–231. Springer, 2015.