Linked bibliography for the SEP article "The Algebra of Logic Tradition" by Stanley Burris and Javier Legris
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- Boole, G., 1847, The Mathematical Analysis of Logic, Being an
Essay Towards a Calculus of Deductive Reasoning, Cambridge:
Macmillan, Barclay, & Macmillan; reprinted Oxford: Basil
Blackwell, 1951. (Scholar)
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Probabilities, London: Macmillan; reprint by Dover 1958. (Scholar)
- –––, 1997. Selected Manuscripts on Logic and
its Philosophy, Ivor Grattan-Guinness and Gérard Bornet
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- Couturat, Louis, 1905, L’Algèbre de la Logique,
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- Dedekind, R., 1897, “Über Zerlegungen von Zahlen durch
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- De Morgan, A., 1847, Formal Logic: or, the Calculus of Inference, Necessary and Probable, London: Taylor and Walton; reprinted London: The Open Court Company 1926. (Scholar)
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- Feferman, S. and R.L. Vaught, 1959, “The first order
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- Frege, F., 1879, Begriffsschrift: eine der arithmetischen
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- Halmos, P.R., 1956a, “Algebraic logic. I. Monadic Boolean
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- –––, 1956c, “Algebraic logic. II.
Homogeneous locally finite polyadic Boolean algebras of infinite
degree”, Fundamenta Mathematica, 43:
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- –––, 1956d, “Algebraic logic. III.
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- –––, 1957, “Algebraic logic. IV. Equality
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- –––, 1962, Algebraic logic, New York:
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- Henkin, L. and J.D. Monk, 1974, “Cylindric algebras and
related structures”, in L. Henkin et al. (eds.), Proceedings
of the Tarski Symposium, Proceedings of Symposia in Pure
Mathematics, vol. XXV, Providence, RI: American Mathematical Society,
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- Henkin, L. and A. Tarski, 1961, “Cylindric algebras”,
in Lattice Theory, Proceedings of Symposia in Pure Mathematics
2, R. P. Dilworth (ed.), Providence, RI: American Mathematical
Society, pp. 83–113. (Scholar)
- Hilbert, D., 1899, The Foundations of Geometry; reprinted Chicago: Open Court 1980, 2nd edition. (Scholar)
- Hilbert, D. and W. Ackermann, 1928, Grundzüge der theoretischen Logik, Berlin: Springer. (Scholar)
- Huntington, E.V., 1904, “Sets of independent postulates for
the algebra of logic”, Transactions of the American
Mathematical Society, 5: 288–309. (Scholar)
- –––, 1933, “New sets of independent
postulates for the algebra of logic, with special reference to
Whitehead and Russell’s Principia Mathematica”, Transactions
of the American Mathematical Society, 35(1): 274–304. (Scholar)
- Jevons, W.S., 1869, The Substitution of Similars, the True Principle of Reasoning, Derived from a Modification of Aristotle’s Dictum, London: Macmillan and Co. (Scholar)
- –––, 1870, Elementary Lessons in Logic,
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- –––, 1874, The Principles of Science, A Treatise on Logic and the Scientific Method, London and New York: Macmillan and Co.; reprinted 1892. (Scholar)
- –––, 1880, Studies in Deductive Logic. A
Manual for Students, London and New York: Macmillan and Co. (Scholar)
- –––, 1883, The Elements of Logic, New York and Chicago: Sheldon & Co. (Scholar)
- –––, 1890, Pure Logic and Other Minor Works, Robert Adamson and Harriet A. Jevons (eds), New York: Lennox Hill Pub. & Dist. Co.; reprinted 1971. (Scholar)
- Jónsson, B. and A. Tarski, 1951, “Boolean Algebras
with Operators. Part I”, American Journal of
Mathematics, 73(4): 891–939. (Scholar)
- Kolata, G., 1996, “Computer Math Proof Shows Reasoning
Power”, The New York Times, December 10 (Technology
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[Available Online] (Scholar)
- Löwenheim, L., 1915, “Über möglichkeiten im
Relativkalül”, Mathematische Annalen, 76(4):
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- –––, 1940, “Einkleidung der Mathematik in Schröderschen Relativkalkul”, Journal of Symbolic Logic, 5: 1–17. (Scholar)
- Macfarlane, A., 1879, Principles of the Algebra of Logic. With Examples, Edinburgh: David Douglas. (Scholar)
- Monk, J. D., 1964, “On Representable Relation
Algebras”, The Michigan Mathematical Journal, 11:
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- Mostowski, A., 1952, “On direct products of theories”, Journal of Symbolic Logic, 17: 1–31. (Scholar)
- Peirce, C.S., 1867, “On an Improvement in Boole’s Calculus
of Logic”, Proceedings of the American Academy of Arts and
Sciences, 7: 250–261; reprinted in Peirce 1933 [CP], vol. III,
pp. 1–19. (Scholar)
- Peirce, C.S., 1870, “Description of a notation for the logic
of relatives, resulting from an amplification of the conceptions of
Boole’s calculus of logic”, Memoirs of the American
Academy, 9: 317–378; reprinted in Collected Papers
1933: Volume III, 27–98. (Scholar)
- –––, 1880, “On the algebra of logic. Chapter I: Syllogistic. Chapter II: The logic of non-relative terms. Chapter III: The logic of relatives”, American Journal of Mathematics, 3: 15–57; reprinted in Collected Papers 1933: Volume III, 104–157. (Scholar)
- –––, 1885, “On the Algebra of Logic: A
Contribution to the Philosophy of Notation”, American
Journal of Mathematics 7(2): 180–202; reprinted in
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- –––, 1933 [CP], Collected Papers, Charles Hartshorne and Paul Weiss (eds.), Cambridge: Harvard University Press. (Scholar)
- Schröder, E., 1890–1910, Algebra der Logik, Vols.
I–III; reprint Chelsea 1966. (Scholar)
- Sheffer, H.M., 1913, “A set of five independent postulates
for Boolean algebras, with application to logical constants”,
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- Skolem, T., 1919, “Untersuchungen über die Axiome des
Klassenkalküls und Über Produktations- und
Summationsprobleme, welche gewisse Klassen von Aussagen
betreffen”, Videnskapsselskapets skrifter, I.
Matematisk-naturvidenskabelig, klasse 3; reprinted in Skolem
1970: 66–101. (Scholar)
- –––, 1920, “Logisch-kombinatorische
Untersuchungen über die Erfülbarkeit oder Beweisbarkeit
mathematischer Sätze nebst einem Theoreme über dichte
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- –––, 1922, “Einige Bemerkungen zur
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Matematikerkongressen i Helsingfors den 4–7 Juli 1922, Den
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- –––, 1928, “Über die mathematische
Logik”, Norsk Mathematisk Tidsskrift, 10:
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- –––, 1970, Selected Works in Logic, Oslo: Universitetsforlaget. (Scholar)
- Stone, M.H., 1936, “The theory of representations for Boolean algebras”, Transactions of the American Mathematical Society, 40(1): 37–111. (Scholar)
- –––, 1937, “Applications of the theory of
Boolean rings to general topology”, Transactions of the
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- Tarski, A., 1941, “On the calculus of relations”, The Journal of Symbolic Logic, 6(3): 73–89 (Scholar)
- Tarski, A. and S. Givant, 1987, Set Theory Without
Variables, (Series: Colloquium Publications, Volume 1),
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- Whitehead, A.N., and B. Russell, 1910–1913, Principia
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- Whitman, P.M., 1941, “Free lattices”, Annals of
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- Wiener, N., 1913, A Comparison between the treatment of the
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- Badesa, Calixto, 2004, The Birth of Model Theory. Löwenheim Theorem in the Frame of the Theory of Relations, Princeton & Oxford: Princeton University Press. (Scholar)
- Brady, Geraldine, 2000, From Peirce to Skolem, Amsterdam et al.: North-Holland. (Scholar)
- Burris. Stanley & H.P. Sankappanavar, 2013, “The Horn
Theory of Boole’s Partial Algebras”, The Bulletin of
Symbolic Logic, 19(1): 97–105. (Scholar)
- Esquisabel, Oscar M., 2012, “Representing and Abstracting.
An Analysis of Leibniz’s Concept of Symbolic Knowledge”, in Abel
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- Gabbay, Dov. M. & John Woods (eds.), 2004, Handbook of the
History of Logic. Volume 3, The Rise of Modern Logic: From Leibniz to
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- Grattan-Guinness, Ivor, 1991, “The Correspondence between George Boole and Stanley Jevons, 1863–1864”, History and Philosophy of Logic, 12(1): 15–35 (Scholar)
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- Hailperin, Theodore, 2004, “Algebraical Logic 1685–1900”, in Gabbay & Woods 2004: 323–388. (Scholar)
- Haaparanta, Leila (ed.), 2009, The Development of Modern Logic, New York and Oxford: Oxford University Press. (Scholar)
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- Legris, Javier, 2012, “Universale Sprache und Grundlagen der
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- Mancosu, Paolo, Richard Zach, and Calixto Badesa, 2009, “The Development of Mathematical Logic from Russell to Tarski: 1900–1935”, in Haaparanta 2009: 318–471 (Scholar)
- Peckhaus, Volker, 1997, Logik, Mathesis universalis und
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- Sánchez Valencia, Victor, 2004, “The Algebra of
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- Van Heijenoort, Jean, 1967, “Logic as Calculus and Logic as Language”, Synthese, 17: 324–330 (Scholar)