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A Study on A Different Formulation of Boolean Structure


Affiliations
1 Department of Philosophy, University of Kalyani. P.O.: Kalyani, Dist.: Nadia, West Bengal, Pin: 741235, India
2 Department of Philosophy, University of Kalyani, P.O. Kalyani, Dist. Nadia, West Bengal, Pin 741235, India
3 epartment of Mathematics, University of Kalyani, P.O. Kalyani, Dist. Nadia, West Bengal, Pin 741235, India
     

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Logic is the main essence of human reasoning. English Scientist and Logician George Boole (1815-1864) initiated the idea of a structure which is based upon some reasoning of difference occurrence in the Universe. Professor Boole wrote a book entitled “The Laws of Thought” which was collection of his papers on such type of reasoning. In this book he formulated a structure upon the interrelationship of element. After his name the structure is known as Boolean Structure. In this paper we present a somewhat different formulation of a Boolean Structure. Further it has been shown in the paper that Associative Laws in a Boolean structure follow from the other axioms of the same i.e., in other words it may be stated that the axiom of Associative Laws in the definition of a Boolean algebra is redundant.

Keywords

Boolean Structure, Another Formulation, Commutative Law, Associative Law.
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  • G. Boole, The Release Date: July 19, 2017. ‘Laws of Thought’, [EBook #15114], URL: https://www.gutenberg.org/files/15114/15114-pdf.pdf. pp.1-344.

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  • A Mukherjee and K Biswas, 2018, ON BOOLEAN LOGIC: A MOTIVATION FROM A FEMALE LOGICIAN, Communicated.

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  • A Study on A Different Formulation of Boolean Structure

Abstract Views: 440  |  PDF Views: 3

Authors

Anindita Mukherjee
Department of Philosophy, University of Kalyani. P.O.: Kalyani, Dist.: Nadia, West Bengal, Pin: 741235, India
Kuheli Biswas
Department of Philosophy, University of Kalyani, P.O. Kalyani, Dist. Nadia, West Bengal, Pin 741235, India
Sanjib Kumar Datta
epartment of Mathematics, University of Kalyani, P.O. Kalyani, Dist. Nadia, West Bengal, Pin 741235, India

Abstract


Logic is the main essence of human reasoning. English Scientist and Logician George Boole (1815-1864) initiated the idea of a structure which is based upon some reasoning of difference occurrence in the Universe. Professor Boole wrote a book entitled “The Laws of Thought” which was collection of his papers on such type of reasoning. In this book he formulated a structure upon the interrelationship of element. After his name the structure is known as Boolean Structure. In this paper we present a somewhat different formulation of a Boolean Structure. Further it has been shown in the paper that Associative Laws in a Boolean structure follow from the other axioms of the same i.e., in other words it may be stated that the axiom of Associative Laws in the definition of a Boolean algebra is redundant.

Keywords


Boolean Structure, Another Formulation, Commutative Law, Associative Law.

References





DOI: https://doi.org/10.24906/isc%2F2018%2Fv33%2Fi1%2F181781