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Biswas, Kuheli
- A Brief Study on Boolean Logic as a Dual Analogue of an Ideal
Abstract Views :372 |
PDF Views:5
Authors
Affiliations
1 UGC-JRF, Department of Philosophy , University of Kalyani, P.O.: Kalyani , Dist: Nadia , PIN: 741235, IN
2 Department of Philosophy, University of Kalyani, P.O.: Kalyani, Dist:Nadia, PIN:741235, IN
3 Department of Mathematics, University of Kalyani, P.O.: Kalyani, Dist:Nadia, PIN:741235., IN
1 UGC-JRF, Department of Philosophy , University of Kalyani, P.O.: Kalyani , Dist: Nadia , PIN: 741235, IN
2 Department of Philosophy, University of Kalyani, P.O.: Kalyani, Dist:Nadia, PIN:741235, IN
3 Department of Mathematics, University of Kalyani, P.O.: Kalyani, Dist:Nadia, PIN:741235., IN
Source
Indian Science Cruiser, Vol 32, No 6 (2018), Pagination: 32-35Abstract
In this paper we wish to establish a Structure termed as Quotient Boolean algebra from the view point of a filter as a dual analogue of an Ideal. Some related properties are also to be developed in this work.Keywords
Boolean Algebra , Principle of Duality, Ideal, Filter.
References
- Boolean Algebra and its Application, John Eldon Whitesitt. Dover Publication.
- Logic and Boolean Algebra, Bradford Henry Arnold, Prentice-Hall, 1962, pp. 1-144
- The Laws of Thought, George Boole, Release Date: July 19, 2017
- G. Boole, An Investigation of the Laws of Thought , Dover Publication , New York , 1958.
- G. Boole, The Laws of Thought , facsimile of 1854 edition, 1854/2003.
- A Study on A Different Formulation of Boolean Structure
Abstract Views :341 |
PDF Views:3
Authors
Affiliations
1 Department of Philosophy, University of Kalyani. P.O.: Kalyani, Dist.: Nadia, West Bengal, Pin: 741235, IN
2 Department of Philosophy, University of Kalyani, P.O. Kalyani, Dist. Nadia, West Bengal, Pin 741235, IN
3 epartment of Mathematics, University of Kalyani, P.O. Kalyani, Dist. Nadia, West Bengal, Pin 741235, IN
1 Department of Philosophy, University of Kalyani. P.O.: Kalyani, Dist.: Nadia, West Bengal, Pin: 741235, IN
2 Department of Philosophy, University of Kalyani, P.O. Kalyani, Dist. Nadia, West Bengal, Pin 741235, IN
3 epartment of Mathematics, University of Kalyani, P.O. Kalyani, Dist. Nadia, West Bengal, Pin 741235, IN
Source
Indian Science Cruiser, Vol 33, No 1 (2019), Pagination: 25-29Abstract
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
- 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.
- F.M. Brown, Boolean Reasoning, ISBN 978-14757-2078-5.
- B.F. Arnold, 1962, Logic and Boolean Algebra, Prentice-Hall, pp. 1-144
- J.E Whitesitt, Boolean Algebra and its Application, Dover Publication.URL: http://store.doverpublications.com/0486477673.html
- Peirce, 1880. “ A Boolean algebra with one constant” , MS collected papers v.4, paragraphs 12-20 reprinted writings v.4, pp. 218-21.
- G. Boole, 1847. Mathematical analysis of logic (Cambridge and London); repr. In studies in logic and probabilities ed. R. Rhees (London 1952).
- G. Boole, 1854. The Laws of Thought ( London and Cambridge ); repr. as Collected Logical Works. Vol. 2 , ( Chicago and London ; Open Court, 1940).
- G Frege, 1882. Boole’s Logical Calculus and the Concept Script, in posthumous writing transl. P. Long and R . White 1969 , pp. 9-46
- A Mukherjee and K Biswas, 2018, ON BOOLEAN LOGIC: A MOTIVATION FROM A FEMALE LOGICIAN, Communicated.
- K Biswas, and A Mukherjee, 2018, An approach made by female logician to the deductive system in Boolean Logic, Communicated.
- A Mukherjee, and K Biswas, 2018, On Boolean Logic as an ordered pair of Boolean Structure and its Filter, Communicated.
- Some Contribution to the Development of Modern Logic of Nineteenth Century
Abstract Views :265 |
PDF Views:4
Authors
Affiliations
1 Department of Philosophy, University of Kalyani, IN
2 Department of Philosophy, University of Kalyani. P.O.: Kalyani, Dist: Nadia, Pin:741235, West Bengal, IN
1 Department of Philosophy, University of Kalyani, IN
2 Department of Philosophy, University of Kalyani. P.O.: Kalyani, Dist: Nadia, Pin:741235, West Bengal, IN
Source
Indian Science Cruiser, Vol 33, No 5 (2019), Pagination: 47-50Abstract
The aim of this paper is to focus on some contributory works of nineteenth century which has remarked as a revolutionary period of modern logic. Modern logic starts with George Boole’s algebra of logic. This paper investigates the later revision made by the followers of Boole for the development of his system and the further periodical development of modern logic.Keywords
Aristotle’s Logic, Algebra of Logic, Modern Logic, Set Theory, Venn Diagram.References
- New World Encyclopedia, Retrieved 18:12, July 23, 2019 from https://www.newworldencyclopedia.org/entry/History_of_logic.
- New World Encyclopedia, Retrieved 18:12, July 23, 2019 from https://www.newworldencyclopedia.org/entry/History_of_logic.
- L. Haaparanta, (2009). The Development of Logic. Oxford University Press
- Ibid.
- L. Haaparanta, (2009). The Development of Logic. Oxford University Press. P-170
- I.M. Bochenski, Trans. And Edt. By Ivo Thomas. (1961) ‘A History of Formal Logic’. University of Notre Dame Press. P 287.
- J. Lukasiewicz, (1957), ARISTOTLE’S SYLLOGISTIC FROM THE STANDPOINT OF MODERN FORMAL LOGIC. Second Edition Enlarged, Oxford University Press. pp 36-37.
- This quotation is taken from Standford Encyclopedia of Philosophy. Simons, Peter, “Jan Łukasiewicz”, The Stanford Encyclopedia of Philosophy (Spring 2017 Edition), Edward N. Zalta (ed.), URL =
- On Some Results in Quotient Boolean Algebra and Boolean Logic
Abstract Views :233 |
PDF Views:82
Authors
Affiliations
1 Department of Philosophy, University of Kalyani, P.O.: Kalyani, Dist:Nadia, PIN:741235, IN
2 Department of Mathematics, University of Kalyani, P.O.: Kalyani, Dist:Nadia, PIN:741235, IN
1 Department of Philosophy, University of Kalyani, P.O.: Kalyani, Dist:Nadia, PIN:741235, IN
2 Department of Mathematics, University of Kalyani, P.O.: Kalyani, Dist:Nadia, PIN:741235, IN
Source
Indian Science Cruiser, Vol 33, No 6 (2019), Pagination: 11-16Abstract
The aim of this paper is to derive some results in quotient Boolean algebra and as a consequence also in Boolean logic. The work carried out in the present paper is in fact an extension of Behara, Biswas and Datta {cf.[1]}.Full Text
References
- Rinku Behara, Kuheli Biswas and Sanjib Kumar Datta, A Brief Study on Boolean Logic as a Dual Analogue of an Ideal, Indian Science Cruiser, Vol. 32, No. 6, November 2018, pp. 32-35.
- Bradford Henry Arnold, Logic and Boolean Algebra, Prentice-Hall, 1962, pp. 1-144
- George Boole, The Laws of Thought, , Release Date: July 19, 2017
- George Boole, An Investigation of the Laws of Thought , Dover Publication , New York , 1958.
- George Boole, The Laws of Thought , facsimile of 1854 edition , 1854/2003.