Publications of D.J. Foulis
1. Involution Semigroups, Ph.D. Thesis, Tulane University,
New Orleans, LA (1958), 114 pp (directed by Fred Wright).
2. Baer *-semigroups, Proc. Amer. Math. Soc. 11 (1960), 648-654.
3. Conditions for the modularity of an orthomodular lattice,
Pacific J. Math. l (1961), 889-895.
4. A note on orthomodular lattices, Portugaliae Mathematica 21
(1962), 65-72.
5. Relative inverses in Baer *-semigroups, Mich. Math. J. 10
(1963), 65-84.
6. Orthomodular Lattices, University of Florida Mimeographed Notes
(1964), 159pp.
7. Semigroups co-ordinatizing orthomodular geometries,
Canadian J. Math. 17 (1965), 40-51
8. Fundamental Concepts of Mathematics, University of Massachusetts
Mathematics Department (1966), 258pp
9. Multiplicative elements in Baer *-semigroups, Math. Annalen 175
(1968), 297-302
10. Fundamental Concepts of Mathematics’, Prindle, Weber, and Schmidt,
Boston (1969), 212 pp., ISBN 87150-075-4
11. An approach to empirical logic, Amer. Math. Mon. 77 (1970),
363-374, (with C.H. Randall).
12. Lexicographic orthogonality, Jour. of Comb. Theory, Ser. A,
11 (1971), 157-162, (with C.H. Randall).
13. Conditioning maps on orthomodular lattices, Glasgow Math. Jour.
12 (1971), 35-42, (with C.H. Randall).
14. Free Baer *-semigroups, Carribean J. of Science and Math. 11,
No. 1 (1972), 25-30.
15. States and the free orthogonality monoid, Math. Systems Theory
6, No. 3 (1972), 268-276, (with C.H. Randall).
16. Operational statistics I - Basic concepts, J. Math. Physics
11 (1972), 1667-1675, (with C.H. Randall).
17. Orthomodular generalizations of homogeneous Boolean algebras,
J. Australian Math. Soc. 15 (1973), 94-104, (with C.H. Randall
and M. Janowitz).
18. Operational statistics II - Manuals of operations and their
logics, J. Math. Physics 14 (1973), 1472-1480, (with C.H. Randall).
19. The stability of pure weights under conditioning, Glasgow Math.
Jour. 15 (1974), 5-12, (with C.H. Randall).
20. The empirical logic approach to the physical sciences, in
Lecture Notes in Physics No. 29, Foundations of Quantum Mechanics
and Ordered Linear Spaces, A. Hartkamper and H. Neumann, eds.,
Springer Verlag, Heidelberg (1974), 230-249, (with C.H. Randall).
21. Empirical logic and quantum mechanics, Synthese 29 (1974),
81-111, (with C.H. Randall).
22. Empirical logic and quantum mechanics, in Logic and Probability
in Quantum Mechanics, P. Suppes, ed., D. Reidel Publishing Co.,
Dordrecht, Holland (1976), (with C.H. Randall).
23. A mathematical setting for inductive reasoning, in Foundations
of Probability Theory, Statistical Inference, and Statistical
Theories of Science III, C. Hooker and W. Harper,eds., D.
Reidel Publishing Co., Dordrecht, Holland (1976), 169-205,
(with C.H.Randall).
24. Calculus, Worth Publishers, Inc. N.Y. (1978), 993 pp,
ISBN 0-87901-087-8 (with M. Munem).
25. Study Guide for Calculus’ (3 volumes), Worth Publishers, Inc.
N.Y. (1978) 359pp, 370pp, 365pp, (with M. Munem).
26. Solutions Manual for Calculus, Worth Publishers, Inc. N.Y.
(1978), 779pp (with M. Munem).
27. The operational approach to quantum mechanics, in The Logico-
Algebraic Approach to Quantum Mechanics’ III, University of
Western Ontario Series in Philosophy of Science’, C. Hooker,
ed., D. Reidel Publishing Co., Dordrecht, Holland (1978),
167-201, (with C.H. Randall).
28. Manuals, morphisms, and quantum mechanics, in Mathematical
Foundations of Quantum Theory, A. Marlow, ed., Academic Press
(1978), 105-126, (with C.H. Randall).
29. Tensor products of quantum logics do not exist, Notices of the
American Math. Society 26, No. 6 (1979), A-557, (with C.H. Randall).
30. Algebra and Trigonometry with Applications, Worth Publishers, Inc.,
N.Y. (1979), 574 pp, ISBN 0-87901-133-5 (with M. Munem).
31. College Algebra, Worth Publishers, Inc., N.Y. (1979), 396pp,
ISBN 0-87901-170-X (with M. Munem).
32. College Trigonometry’, Worth Publishers, Inc., N.Y. (1979),
300 pp, ISBN 0-87901-171-8 (with M. Munem).
33. Weight functions on extensions of the compound manual, Glasgow
Math. Jour. 21 (1980), 97-101, (with P. Frazer and C.H. Randall).
34. Empirical logic and tensor products, in Interpretations and
Foundations of Quantum Theory, H. Neumann, ed., Wissenschafts-
verlag, Bibliographisches Institut, Band 5, Mannheim/Wien/Zurich
(1981), 9-20, (with C.H. Randall).
35. Operational statistics and tensor products, in Interpretations
and Foundations of Quantum Theory’, H. Neumann, ed., Band 5,
Wissenschaftsverlag, BibliographischesInstitut, Mannheim/Wien/
Zurich (1981), 21-28, (with C.H. Randall).
36. What are quantum logics and what ought they to be?, in Current
Issues in Quantum Logic, E. Beltrametti and B. van Fraassen, eds.,
Ettore Majorana International Science Series 8, Plenum Press, NY
(1981), 35-52, (with C.H. Randall).
37. Realism, operationalism, and quantum mechanics, Foundations of
Physics 13, Issue 8 (1983), 813-842, (with C.H. Randall and
C. Piron).
38. Properties and operational propositions in quantum mechanics,
Foundations of Physics 13, Issue 8 (1983) 843-863, (with C.H.
Randall).
39. A mathematical language for quantum physics, in Transactions of
the 25 Cours de Perfectionnement de l'Association’ Vaudoise
des Chercheurs in Physique; Les Fondements de la Mecanique
Quantique, Montana, Switzerland, C. Gruber, C. Piron, T. Minhtom,
and R. Weil, eds. (1983), 193-226, (with C.H. Randall).
40. A note on misunderstandings of Piron's axioms for quantum mechanics,
Foundations of Physics 14, Issue 1 (1984), 65-81, (with C.H. Randall).
41. Stochastic entities, in Transactions of the International Symposium
on Quantum Logic, University of Cologne, P. Mittelstaedt and E.
Stachow, eds., Wissenschaftsverlag, Bibliographisches Institut 6,
Mannheim/Wien/Zurich (1984), 265-284, (with C.H. Randall).
42. Dirac revisited, in Transactions of the Symposium on the
Foundations of Modern Physics, Joensuu, Finland, P. Lahti and
P. Mittelstaedt, eds., World Scientific Publishing Co., Singapore
(1985), 97-112, (with C.H. Randall).
43. Tensor products and probability weights, International Jour. of
Theoretical Physics 26, No. 3 (1987), 199-219 (with C.H. Randall
and M. Klaey).
44. After Calculus: Algebra, Dellen/Macmillan, N.J. (1988), 488 pp,
ISBN 0-02-384790-5 (with M. Munem).
45. After Calculus: Analysis, Dellen/Macmillan, N.J. (1989), 556 pp,
ISBN 0-02-339130-8 (with M. Munem).
46. Coupled physical systems, Foundations of Physics 7 (1989),
905-922
47. Charles Hamilton Randall, Foundations of Physics 20 No. 5 (1990),
473-476 (with M.K. Bennett).
48. Superposition in Quantum and Classical Mechanics, Foundations of
Physics 20 No. 6 (1990), 733-744 (with M.K. Bennett).
49. Maximum liklihood estimation on generalized sample spaces; An
alternative resolution of Simpson's paradox, Foundations of
Physics 20 No. 7 (1990), 777-799 (with M.P. Klaey).
50. Stochastic quantum mechanics viewed from the language of manuals,
Foundations of Physics 20 No. 7 (1990), 823-858 (with F. Schroeck,
Jr.).
51. Algebra and Trigonometry with Applications, 3rd Edition, Worth
Publishers, N.Y. (1992), 720 pp, ISBN 0-87901-498-9 (with M. Munem).
52. College Algebra, Worth Publishers, N.Y. (1992), 3rd Edition,
496 pp, ISBN 0-87901-499-7 (with M. Munem).
53. Filters and supports in orthoalgebras, International Jour. of
Theoretical Physics 31, No. 5 (1992), 789-802 (with R.J. Greechie
and G.T. Ruettimann).
54. Tensor products of quantum logics, in The Interpretation of
Quantum’ ’Theory: Where Do We Stand?, Luigi Accardi, ed.,
Istituto Della Enciclopedia Italiana, Rome (1994) 303-316,
ISBN 88-12-00019-3.
55. Logicoalgebraic structures II. Supports in test spaces,
International J. of Theoretical Physics 32, No. 10 (1993)
1675-1690 (with R.J. Greechie and G.T. Ruettimann).
56. Tensor products of orthoalgebras, Order 10 (1993) 271-282
(with M.K. Bennett)…
57. Effect algebras and unsharp quantum logics, Foundations of
Physics 24, No. 10 (1994) 1325-1346 (with M.K. Bennett).
58. Interval algebras and unsharp quantum logics, University
of Massachusetts Mimeographed Notes (1992) (with M.K. Bennett).
59. Sums and products of interval algebras, International Jour.
of Theoretical Physics, 33, No. 11 (1994) 2119-2136 (with M.K.
Bennett and R.J. Greechie).
60. The center of an effect algebra, Order 12 (1995) 91-106 (with
R.J. Greechie and S. Pulmannova).
61. On absolute compatibility and hidden variables in quantum logics,
to appear in Czech Math. J. (with P. Ptak)
62. On the tensor product of a Boolean algebra and an orthoalgebra,
Czech Math. J. 45, 120 (1995) 117-126 (with P. Ptak).
63. The transition to effect algebras, International Jour. of
Theoretical Physics, 34, No. 8 (1995) 1-14 (with R.J. Greechie).
64. Phi-Symmetric Effect Algebras, Foundations of Physics 25, No.12
(1995) 1701-1724 (with M.K. Bennett).
65. Test Groups, International J. of Theoretical Physics 35, No. 5
(1996) 1117-1140 (with M.K. Bennett and R.J. Greechie).
66. Interval and scale effect algebras, to appear in Advances in
Applied Mathematics (with M.K. Bennett).
67. Quotients of interval effect algebras, International J. of
Theoretical Physics 35, No. 11, (1996) 2321-2338 (with M.K.
Bennett and R.J. Greechie).
68. Mathematical metascience, to appear in University of London,
Journal of Natural Geometry, January 1998.
69. A half-century of quantum logic, what have we learned?, to
appear in Proceedings of the Conference Einstein Meets Magritte,
Brussels in June 1995.
70. Quantum Logic, in Encyclopedia of Applied Physics, George L. Trigg,
ed., VCH Publishers, Weinheim, Germany, NY, in collaboration with
the American Institute of Physics, the German Physical Society,
The Japan Society for Applied Physics, and the Physical Society
of Japan, vol. 15, (1996) 229-241 (with R.J. Greechie).
71. The transition to unigroups, submitted to International Journal
of Theoretical Physics.