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The development of Indian logic dates back to the Chandahsutra of Pingala and anviksiki of Medhatithi Gautama (c. 6th century BCE); the Sanskrit grammar rules of Pāṇini (c. 5th century BCE); the Vaisheshika school's analysis of atomism (c. 6th century BCE to 2nd century BCE); the analysis of inference by Gotama (c. 6th century BC to 2nd century CE), founder of the Nyaya school of Hindu ...
Tarka-Sangraha (IAST: Tarka-saṅgraha) is a treatise in Sanskrit giving a foundational exposition of the Indian system of logic and reasoning.The work is authored by Annambhatta and the author himself has given a detailed commentary, called Tarka-Sangraha Deepika, for the text.
Boolean algebra is a mathematically rich branch of abstract algebra. Stanford Encyclopaedia of Philosophy defines Boolean algebra as 'the algebra of two-valued logic with only sentential connectives, or equivalently of algebras of sets under union and complementation.' [1] Just as group theory deals with groups, and linear algebra with vector spaces, Boolean algebras are models of the ...
In mathematics and mathematical logic, Boolean algebra is a branch of algebra.It differs from elementary algebra in two ways. First, the values of the variables are the truth values true and false, usually denoted 1 and 0, whereas in elementary algebra the values of the variables are numbers.
The term "Boolean algebra" honors George Boole (1815–1864), a self-educated English mathematician. He introduced the algebraic system initially in a small pamphlet, The Mathematical Analysis of Logic, published in 1847 in response to an ongoing public controversy between Augustus De Morgan and William Hamilton, and later as a more substantial book, The Laws of Thought, published in 1854.
Chapter 18 contained 103 Sanskrit verses which began with rules for arithmetical operations involving zero and negative numbers [74] and is considered the first systematic treatment of the subject. The rules (which included a + 0 = a {\displaystyle a+0=\ a} and a × 0 = 0 {\displaystyle a\times 0=0} ) were all correct, with one exception: 0 0 ...
Boolean function with two different minimal forms. The Blake canonical form is the sum of the two. In Boolean logic , a formula for a Boolean function f is in Blake canonical form ( BCF ), [1] also called the complete sum of prime implicants , [2] the complete sum , [3] or the disjunctive prime form , [4] when it is a disjunction of all the ...
The primary algebra (Chapter 6 of LoF), whose models include the two-element Boolean algebra (hereinafter abbreviated 2), Boolean logic, and the classical propositional calculus; Equations of the second degree (Chapter 11), whose interpretations include finite automata and Alonzo Church 's Restricted Recursive Arithmetic (RRA).