Abstract
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.
Partially supported by project DGES PB96-0098-C04 (Spain).
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
References
Adams, V., Loustanau, P., An Introduction to Gröbner bases. Graduate Studies in Mathematics 3. Providence, RI, American Mathematical Society Press (1994).
Alonso, J.A., Briales, E., Lógicas polivalentes y bases de Gröbner. In: Vide, M. (ed), Proceedings of the V Congress on Natural Languages and Formal Languages (1989), 307–315. Barcelona, Spain, P.P.U. Press.
Boole, G, An address on the genius and discoveries of Sir Isaac Newton (Lincoln, 1835).
Boole, G., On certain theorems in the calculus of variations. The Cambridge Mathematical Journal 2 (1841), 97–102.
Boole, G., Researches on the theory of analytical transformations with a special application to the reduction of the general equation of the second order. The Cambridge Mathematical Journal 2 (1841), 67–73.
Boole, G., On the integration of linear differential equations with constant coefficients. The Cambridge Mathematical Journal 2 (1841), 114–119.
Boole, G., On a general method in analysis, Philosophical Transactions of the Royal Society of London 134 (1844), 225–286.
Boole, G., On the equations of Laplace’s function. The Cambridge and Dublin Mathematical Journal 1 (1846), 10–22.
Boole, G., On a certain symbolical equation. The Cambridge and Dublin Mathematical Journal 2 (1847), 7–12.
Boole, G., The mathematical analysis of logic, being an essay towards a calculus of deductive reasoning, Cambridge and London (1847), 4–5. Reprinted in: Boole, G., Studies in Logic and Probability, Ed. R. Rhees, London (1952).
Capani, A., Niesi, G., CoCoA user’s manual, Dept. of Mathematics University of Genova (1996).
Chazarain, J., Riscos, A., Alonso, J.A., Briales, E.. Multivalued logic and Gröbner bases with applications to modal logic. Journal of Symbolic Computation 11 (1991) 181–194.
Cobham ed, E.M., Mary Everest Boole, Collected works (4 vols.), London (1931).
Cobham, E.M., Mary Everest Boole, A Memoir with some letters, Ashingdon (1951).
Daniel, F., A Teacher of Brain Liberation, London (1923).
De Morgan, A., On the structure of the syllogism, Trans. Cambridge Phil. Soc., 8 (1846), 379–408. Reprinted in: On the syllogism (edited with an introduction by Peter Heath), London (1966), 1–17.
Diagne, S. B., Boole, 1815-1864; l'oisseau de nuit en plein jour, Belin, Paris (1989)
Everest, M., Home side of a scientific mind (1878); Cobham’s Mary Everest’s Collected Works,, 1–48. Reprinted from The Dublin University Magazine, 91 (1878), 103–114, 173-183, 327-336, 454-460.
Everest, M.: Logic taught by love, rhythm in nature and education (printed 1890, publ. 1905); Cobham’s Mary Everest’s Collected Works, vol. 2, 438.
Everest, M.: Indian thought and western science in the nineteenth century (written 1901, publ. 1909), Cobham’s Mary Everest’s Collected Works, vol. 3, 962.
Everest, M., The nineties (publ. or read 1890-1899), Cobham’s Mary Everest’s Collected Works, vol 2, 565.
Everest, M., On education, Cobham’s Mary Everest’s Collected Works, vol 2, 789.
Grattan-Guinness, I., Mathematics and mathematical physics at Cambridge 1815-40: a survey of the achievements and of the French influence. In: Harman, P.M. (ed.), Wranglers and Physicists, Manchester (1985), 84–111.
Gregory, D.F., Demonstrations, by the method of separation of symbols of theorems in the differential calculus and calculus of finite differences. The Cambridge Mathematical Journal 1 (1838), 232–244.
Gregory, D.F., On the real nature of symbolical algebra. Transactions of the Royal Society of Edinburgh 14 (1840, read 7th May 1838), 208–216.
Hamilton, W., On the study of mathematics, as an exercise of the mind. Discussions on Philosophy and Literature, London (1852), 257–313. Reprinted from: Edinburgh Review, 62 (1836), 409–455.
Harley, R., George Boole, F.R.S., British Quart. Rev. (1866). Reprinted in: Studies in Logic and Probability. Boole’s Collected Logical Works, 425–472.
Kneale, W., Boole and the revival of logic, Mind, 58 (1948), 149–175 (155).
Kobloch, E., Symbolik und Formalismus im mathematischen Denken des 19. und beginnenden 20. Jahrhunderts. In: Dauben, J.M. (ed.), Mathematical perspectives. Essays on Mathematics and its historical development, New York (1981), 139–165.
Koppelman, E., The calculus of operations and the rise of abstract algebra. Archive for the History of Exact Sciences 8 (1971), 155–242.
Laita, L. M., A study of the genesis of Boole’s logic, Doctoral Dissertation, University of Notre Dame, University Microfilms International (76-4613), An Arbor Michigan, London (1976).
Laita, L. M., The influence of Boole’s search for a universal method in analysis on the creation of his logic. Annals of science 34 (1977), 163–176.
Laita, L. M., Influences on Boole’s logic: the controversy between William Hamilton and Augustus De Morgan, Annals of Science 36 (1979), 45–65.
Laita, L. M., Boolean algebra and its extralogical sources: The testimony of Mary Everest Boole, History and Philosophy of Logic 1 (1980), 37–60.
Laita, L.M., E. Roanes-Lozano, L. de Ledesma, J.A. Alonso: A Computer algebra approach to verification and deduction in many-valued knowledg systems. Soft Computing 3/1 (1999), 7–19
Laita, L. M., de Ledesma, L., Roanes-Lozano, E., Pérez, A., Brunori, A., Boole’s logic revisited from computer algebra, Mathematics and Computers in Simulation 51 (2000), 419–439.
de Ledesma, L., Pérez, A., Borrajo, D., Laita, L. M., A computational approach to George Boole’s discovery of mathematical logic, Artificial Intelligence 91 (1997), 281–307.
MacFarlane, A., Lectures on ten British mathematicians of the nineteenth century (New York, 1916) 50–63.
MacHale, D., George Boole, his life and work, Boole Press, Dublin (1985).
Mansel H.L., Veitch, J. (Eds.), Lectures on metaphysics and logic (4 vols.), vols 3 and 4, Edinburgh and London (1859-1861).
Panteki, M., Relationships between algebra, differential equations, and logic in England 1808-1860. Ph.D. Thesis, Council for National Academic Awards, UK (1991)(chapter 4).
Pycior, H.M., Peacock and the British origins of symbolical algebra, Historia Mathematica 8 (1981), 23–45.
Roanes-Lozano, E., Laita, L.M., Roanes-Macías, E., A polynomial model for multivalued logics with a touch of algebraic geometry and computer algebra. Mathematics and Computers in Simulation 45/1-2 (1998), 83–99.
Taylor, G., George Boole F.R.S., 1815-1864, Notes and records of the Royal Society of London, 12 (1956), 44–52 (47). Also in: Harley’s biography, 428.
Whewell, W., Thoughts on the study of mathematics as part of a liberal education, Cambridge (1835).
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2001 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Laita, L.M., de Ledesma, L., Roanes-Lozano, E., Brunori, A. (2001). George Boole, a Forerunner of Symbolic Computation. In: Campbell, J.A., Roanes-Lozano, E. (eds) Artificial Intelligence and Symbolic Computation. AISC 2000. Lecture Notes in Computer Science(), vol 1930. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-44990-6_1
Download citation
DOI: https://doi.org/10.1007/3-540-44990-6_1
Published:
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-42071-2
Online ISBN: 978-3-540-44990-4
eBook Packages: Springer Book Archive