The Monty Hall Problem and beyond: Digital-Mathematical and Cognitive Analysis in Boole’s Algebra, Including an Extension and Generalization to Related Cases

References

[1] J. Rosenhouse, “The Monty Hall Problem: The Remarkable Story Behind Math’s Most Contentious Brainteaser,” Oxford University Press, New York and Oxford, 2009.

[2] J. Gill, “Bayesian Methods,” International Encyclopedia of Statistical Science, Springer, Berlin and New York, 2010, pp. 8-10.

[3] R. D. Gill, “The Monty Hall Problem Is not a Probability Puzzle (It’s a Challenge in Mathematical Modelling),” Statistica Neerlandica, Vol. 65, No. 1, 2010, pp. 57-71. doi:10.111/j.1467-9574.2010.00474.x

[4] J. S. Rosenthal, “Monty Hall, Monty Fall, Monty Crawl,” Math Horizons, Vol. 16, No. 1, September Issue, 2008, pp. 5-7.

[5] I. Grattan-Guinness, “The Search for Mathematical Roots,” Princeton University Press, Princeton and Oxford, 2000.

[6] “The symbols for “and” (+) and “or” (–), and for closed-“true” (0) and open-“false” (1) as used in switching algebra, are the inverse of the conventions used in the algebra of logic. However, because of the perfect duality inherent in the algebra, the pos-tulates and theorems are not affected” (W. Keister, A.E. Ritchie, S.H. Washburn, “The Design of Switching Circuits,” The Bell Telephone Laboratories Series, D. Van Nostrand Company, New York, Toronto, and London, 1951, p. 70 note *).

[7] M. Helft, “Google Can Now Say No to ‘Raw Fish Shoes’ in 52 Languages,” The New York Times, March 9, 2010, pp. A1 and A3.

[8] L. Depuydt, “The Other Mathematics: Language and Logic in Egyptian and in General,” Gorgias Press, Piscataway, New Jersey, 2008, pp. 93-95.

[9] J. Venn, “Symbolic Logic,” 2nd Edition, Macmillan and Company, London and New York, 1894, pp. 245-255.

[10] E. Schroeder, “Vorlesungen über die Algebra der Logik (Exakte Logik),” J. C. Hinrichs, Leipzig, Vol. 1, 1890, p. 319.

[11] L. Depuydt, “Zur unausweichlichen Digitalisierung der Sprachbetrachtung: ‘Allein,’ ‘anderer,’ ‘auch,’ ‘einziger,’ ‘(seiner)seits,’ und ‘selbst’ als digitales Wort-feld im ?gyptisch-Koptischen und im Allgemeinen” (“On the Unavoidable Digitalization of Language Analysis: ‘Alone,’ ‘Other,’ ‘Also,’ ‘Only,’ ‘On (his) part,’ and ‘Self’ as a Lexical Field of Digital Purport in Egyptian-Coptic and in General”), to appear in the series Aegyptiaca Monasteriensia as part of the acts of the Workshop “Lexical Fields, Se

[12] L. Depuydt, “The Other Mathematics: Language and Logic in Egyptian and in General,” Piscataway, New Jersey, 2008, pp. 285-306.

[13] Th. Hailperin, “Boole’s Logic and Probability,” North- Holland Publishing Company, New York and Oxford, 1976, p. 131. Also see the 2nd edition, 1986, p. 215.