**Foundation of BOOLIANS**
In mathematics and mathematical logic, Boolean algebra is the branch of algebra in which the values of the variables are the truth values true and false, usually denoted 1 and 0 respectively. Boolean algebra was introduced by George Boole in his first book The Mathematical Analysis of Logic (1847), and set forth more fully in his An Investigation of the Laws of Thought (1854). According to Huntington, the term "Boolean algebra" was first suggested by Sheffer in 1913. Boole's algebra predated the modern developments in abstract algebra and mathematical logic; it is however seen as connected to the origins of both fields. In an abstract setting, Boolean algebra was perfected in the late 19th century by Jevons, Schröder, Huntington, and others until it reached the modern conception of an (abstract) mathematical structure. In fact, M. H. Stone proved in 1936 that every Boolean algebra is isomorphic to a field of sets.
In the 1930s, while studying switching circuits, Claude Shannon observed that one could also apply the rules of Boole's algebra in this setting, and he introduced switching algebra as a way to analyze and design circuits by algebraic means in terms of logic gates. Shannon already had at his disposal the abstract mathematical apparatus, thus he cast his switching algebra as the two. Efficient implementation of Boolean functions is a fundamental problem in the design of combinational logic circuits. Modern electronic design automation tools for VLSI circuits often rely on an efficient representation of Boolean functions known as (reduced ordered) binary decision diagrams (BDD) for logic synthesis and formal verification.
Logic sentences that can be expressed in classical propositional calculus have an equivalent expression in Boolean algebra. Boolean algebra is not sufficient to capture logic formulas using quantifiers, like those from first order logic. Although the development of mathematical logic did not follow Boole's program, the connection between his algebra and logic was later put on firm ground in the setting of algebraic logic, which also studies the algebraic systems of many other logics. The problem of determining whether the variables of a given Boolean (propositional) formula can be assigned in such a way as to make the formula evaluate to true is called the Boolean satisfiability problem (SAT), and is of importance to theoretical computer science, being the first problem shown to be NP-complete. The closely related model of computation known as a Boolean circuit relates time complexity (of an algorithm) to circuit complexity. Boolean algebra has been fundamental in the development of digital electronics, and is provided for in all modern programming languages. It is also used in set theory and statistics. This is how the different forms of Boolean algebra inspired and forms the verse world of automation in analogue and digital electronics. This automation world is the base of our company. This is how the company’s name fall upon Boolean algebra and named as BOOLIANS.
The company is running in the world of automation since 1998. The present Director of the Company is Tamasi Chatterjee. The soul of the company that is the present technical person of the company is Anjan Chatterjee. |