George Boole, a Forerunner of Symbolic Computation

We examine in this invited presentation Boole's principles of logic and his method of performing inferences. The principles of Boole's logic are based on the application of an early symbolic calculus known in his time as the "method of separation of symbols". His logic's inference procedures are symbolic operations allowed inside this method. Such inference procedures are reinterpreted and generalized using computer algebra. The lecture also presents a short biography of Boole and a description of some of the factors that had an influence on the genesis of his logic.

[1]  José Antonio Alonso Jiménez,et al.  Lógicas polivalentes y bases de Gröbner , 1990 .

[2]  George Boole,et al.  Studies in logic and probability , 1952 .

[3]  Elaine Koppelman,et al.  The calculus of operations and the rise of abstract algebra , 1971 .

[4]  Desmond MacHale,et al.  George Boole: His Life and Work , 1985 .

[5]  Luis M. Laita Influences on Boole's logic: The controversy between William Hamilton and Augustus De Morgan , 1979 .

[6]  D. F. Gregory X.—On the Real Nature of Symbolical Algebra , 1839 .

[7]  Philippe Loustaunau,et al.  Modules and Gröbner bases , 1994 .

[8]  Mary Everest Boole Indian Thought and Western Science in the Nineteenth Century , 1901 .

[9]  E. Roanes-Lozano,et al.  A computer algebra approach to verification and deduction in many-valued knowledge systems , 1999, Soft Comput..

[10]  L. M. Laita,et al.  A polynomial model for multi-valued logics with a touch of algebraic geometry and computer algebra , 1998 .

[11]  H. L. Mansel,et al.  Lectures on metaphysics and logic , 1859 .

[12]  Luis M. Laita Boolean algebra and its extra-logical sources: the testimony of mary everest boole , 1980 .

[13]  William Kneale,et al.  IV.—BOOLE AND THE REVIVAL OF LOGIC , 1948 .

[14]  Mary Everest Boole,et al.  Mary Everest Boole: Collected Works , 1933, The Mathematical Gazette.

[15]  Aurora Pérez,et al.  Boole's logic revisited from computer algebra , 2000 .

[16]  Aurora Pérez,et al.  A Computational Approach to George Boole's Discovery of Mathematical Logic , 1997, Artif. Intell..

[17]  Alexander Macfarlane Lectures on Ten British Mathematicians of the Nineteenth Century , 1917 .

[18]  George Boole,et al.  VIII. On a general method in analysis , 1844, Philosophical Transactions of the Royal Society of London.

[19]  Geoffrey Ingram Taylor George Boole, F. R. S., 1815-1864 , 1956, Notes and Records of the Royal Society of London.

[20]  W. Donkin,et al.  IV. On the equation of Laplace’s functions, &c , 1857, Philosophical Transactions of the Royal Society of London.

[21]  Helena M. Pycior,et al.  George Peacock and the British origins of symbolical algebra , 1981 .

[22]  Luis M. Laita The Influence of Boole’s Search for a Universal Method in Analysis on the Creation of His Logic , 1977 .

[23]  Emilio Briales Morales,et al.  Multi-Valued Logic and Gröbner Bases with Applications to Modal Logic , 1991, J. Symb. Comput..

[24]  Philip H. Demp,et al.  A mathematical perspective , 2001 .

[25]  Eberhard Knobloch Symbolik und Formalismus im mathematischen Denken des 19. und beginnenden 20. Jahrhunderts , 1981 .