A computational approach to George Boole's discovery of Mathematical Logic

Artificial Intelligence

Volumn 91, Issue 2, 1997, Pages 281-307

  De Ledesma, Luis ^a   Pérez, Aurora ^a   Borrajo, Daniel ^b   Laita, Luis M ^a  

^a UNIVERSIDAD POLITÉCNICA DE MADRID   (Spain)

^b UNIVERSIDAD CARLOS III DE MADRID   (Spain)

Author keywords

[No Author keywords available]

Indexed keywords

ALGEBRA; COMPUTATIONAL METHODS; DIFFERENTIATION (CALCULUS); GEOMETRY; MATHEMATICAL MODELS;

ALGEBRAIC EQUATIONS; COMPUTATIONAL MODEL; MATHEMATICAL LOGIC;

ARTIFICIAL INTELLIGENCE;

EID: 0031122241     PISSN: 00043702     EISSN: None     Source Type: Journal    
DOI: 10.1016/S0004-3702(97)00017-9     Document Type: Article

References (35)

1. Working Notes of the AAAI Spring Symposium on Systematic Methods of Scientific Discovery, Stanford University, Stanford, CA (1995).
2. G. Boole, An Address on the Genius and Discoveries of Sir Isaac Newton (Gazete Office, Mechanics Institution, Lincoln, 1835).
3. G. Boole, The Mathematical Analysis of Logic, Being an Essay towards a Calculus of Deductive Reasoning (Macmillan, Barclay and Macmillan, 1847).
4. G. Boole, The Claims of Science, Especially as Founded in its Relation to Human Nature (Taylor, Walton and Maberley, London, 1851).
5. G. Boole, An Investigation of the Laws of Thought, On Which Are Founded the Mathematical Theories of Logic and Probabilities (Walton and Maberley, London and Cambridge, 1854).
6. L. de Ledesma and L.M. Laita, G. Boole, From differential equations to mathematical logic, in: Actas de la Reunión Matemática en Honor de A. Dou, Madrid (Publicaciones de la Universidad Complutense de Madrid, 1989) 341-352.
7. L. de Ledesma, L.M. Laita, A. Pérez and D. Borrajo, Descubrimiento científico e inteligencia artificial, in: Real Academia de Ciencias Exactas, Físicas y Naturales, Proceedings of the Segundo Curso de Conferencias Sobre Inteligencia Artificial (1993) 115-132.
8. L. de Ledesma, A. Pérez, D. Borrajo and L.M. Laita, La lógica de Boole como consecuencia del método de separación de símbolos de Gregory Boole. Estudio histórico y su emulación por computador, in: Contra los titanes de la rutina. Contre les titans de la routine. Proceedings of the Congreso Hispano-Francés Sobre la Historia y la Filosofía de la Matemática (Comunidad de Madrid/CSIC, 1994) 287-300.
9. A. De Morgan, Formal Logic or The Calculus of Inference Necessary and Probable (Taylor and Walton, London, 1847).
10. S. De Morgan, Memoir of Augustus De Morgan (Longman, Essex, 1882).
11. S. Bachir Diagne, Boole: L'Oiseau de Nuit en Plein Jour (Belin, Paris, 1989).
12. M. Everest, Home side of a scientific mind, The Dublin University Magazine 91 (1878) 103-114, 173-183, 327-336, 456-460; Reprinted in Mary Everest Collected Works.
13. M. Everest, Home side of a scientific mind, The Dublin University Magazine 91 (1878) 103-114, 173-183, 327-336, 456-460; Reprinted in Mary Everest Collected Works.
14. D.F. Gregory, Demonstrations, by the method of separation of symbols of theorems in the differential calculus and calculus of finite differences, Cambridge Math. J. 1 (1838) 232-244.
15. D.F. Gregory, On the elementary principles of the application of algebraic symbols to geometry, Cambridge Math. J. 2 (1839) 1-9.
16. W. Hamilton, Lectures on Metaphysics and Logic, Vol. 4 (W. Blackwood and Sons, Edinburgh and London, 1862).
17. R. Harley, G. Boole, British Quarterly Review (July 1886); Reprinted in: R. Harley, Studies in Logic and Probability. Boole's Collected Logical Works, pp. 425-472.
18. R. Harley, G. Boole, British Quarterly Review (July 1886); Reprinted in: R. Harley, Studies in Logic and Probability. Boole's Collected Logical Works, pp. 425-472.
19. W. Kneale and M. Kneale, The Development of Logic (Clarendon Press, Oxford, 1961).
20. E. Knobloch, Symbolik und Formalismus im mathematischen Denken des 19. und beginnenden 20. Jahrhunderts, in: Mathematical Perspectives, Essays on Mathematics and its Historical Development (J.M. Dauben, New York, 1981) 208-216.
21. E. Koppelman, The calculus of operations and the rise of abstract algebra, Archive for the History of Exact Sciences 8 (1971).
22. D. Kulkarni and H.A. Simon, The processes of scientific discovery: the strategy of experimentation, Cognitive Sci. 12 (1988) 139-175.
23. L.M. Laita, The influence of Boole's search for a universal method in analysis on the creation of his logic, Annals of Science (1977) 163-176.
24. L.M. Laita, Influences on Boole's logic, The controversy Hamilton-De Morgan, Annals of Science (1979) 45-65.
25. L.M. Laita, Boolean algebras and its extralogical sources, History and Philosophy of Logic (1980) 37-60.
26. P.W. Langley, J.M. Zytkow, H.A. Simon and G.L. Bradshaw, The search for regularity: four aspects of scientific discovery, in: R.S. Michalski, T.M. Mitchell and J.G. Carbonell, eds., Machine Learning 2 (Morgan Kaufmann, Los Altos, CA, 1986) 425-469.
27. P.W. Langley, J.M. Zytkow, H.A. Simon and G.L. Bradshaw, Scientific Discovery. Computational Explorations of the Creative Processes (MIT Press, Cambridge, MA, 1987).
28. D.B. Lenat, Automated theory formation in mathematics, in: Proceedings IJCAI-77, Cambridge, MA (1977).
29. D.B. Lenat, The nature of heuristics, Artificial Intelligence 19 (1982) 189-249.
30. D.B. Lenat, Eurisko: A program that learns new heuristics and domain concepts, Artificial Intelligence 21 (1983) 61-98.
31. D. MacHale, G. Boole, His Life and Work (Boole Press, Dublin, 1985).
32. M. Panteki, Relationships between algebra, differential equations and logic in England, 1800-1860, Ph.D. Thesis, Council for National Academic Awards, UK (1991).
33. P. Shell and J.G. Carbonell, FRuleKit: A frame-based production system, User's manual, Internal paper (1989).
34. W.M. Shen, Functional transformations in AI discovery systems, Artificial Intelligence 41 (1990) 257-272.
35. J. Shrager and P. Langley, Computational Models of Scientific Discovery and Theory Formation (Morgan Kaufmann, Los Altos, CA, 1990).