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Dick Greechie

Professor, Ph.D. 1966, University of Florida


Research Interests:   Orthomodular lattices and posets,   mathematical foundations of quantum mechanics,   orthogonally spaces,   quantum logic,   empirical logic,   mathematical anthropology.

Publications

  1. J. Su, W. Feng, R. J. Greechie, Distributivity Conditions and the Order-Skeleton of a Lattice, Submitted to Algebra Universallis

  2. W. Feng, J. Su, R. J. Greechie, On Calculating Residuated Approximations, Submitted to Algebra Universallis

  3. K. J. Al-Agha and R. J. Greechie, Order Dimension of Orthomodular Amalgamations Over Trees, Order, 25 (2008), No. 1, 55-68.

  4. J. C. Carréga and R. J. Greechie, Coverings of [MOn] and Minimal Orthomodular Lattices, Algebra Universalis, 58 (2008), No. 4, 427-459.

  5. D. J. Foulis and R. J. Greechie, Quantum Logic and Partially Ordered Abelian Groups, a book chapter in Handbook of Quantum Logic and Quantum Structures, Elsevier, 2007, 215-283.

  6. K. J. Al-Agha and R. J. Greechie, States on Orthomodular Amalgamations Over Trees, International Journal of Theoretical Physics, 45 (2006), No. 2, 271-283.

  7. R. J. Greechie and B. J. Legan, Three Classes of Orthomodular Lattices, International Journal of Theoretical Physics, 45 (2006), No. 2, 351-357.

  8. S. P. Gudder and R. J. Greechie, Uniqueness and Order in Sequential Effect Algebras, International Journal of Theoretical Physics, 44 (2005), No. 7, 755-770.

  9. R. J. Greechie, S. Pulmannová, and K. Svozil, Preface to the Proceedings of Quantum Structures 2002, International Journal of Theoretical Physics, 44 (2005), No. 7, 691-692.

  10. D. J. Foulis and R. J. Greechie, Semisimplicial Unital Groups, International Journal of Theoretical Physics, 43 (2004), 1689-1704.

  11. M. D. Chiara, R. Giuntini, and R. J. Greechie, Reasoning in Quantum Theory Sharp and Unsharp Quantum Logics, Trends in Logic, Vol. 22, Kluwer, Dordrecht/Boston/London, 2004.

  12. S. P. Gudder and R. J. Greechie, Sequential Products on Effect Algebras, Reports on Mathematical Physics, 49 (2002), No. 1, 87-111.

  13. K. J. Al-Agha and R. J. Greechie, The Involutory Dimension of Involution Posets, Order, 18 (2001), No. 4, 323-337.

  14. D. J. Foulis and R. J. Greechie, Specification of Finite Effect Algebras, International Journal of Theoretical Physics, 39 (2000), No. 3, 665-676.

  15. J. C. Carréga, R. J. Greechie, and R. Mayet, Minimal Orthomodular Lattices From Quadratic Spaces Over Finite Fields, International Journal of Theoretical Physics, 39 (2000), No. 3, 517-524.

  16. D. J. Foulis and R. J. Greechie, Probability Weights and Measures on Finite Effect Algebras, International Journal of Theoretical Physics, 38 (1999), No. 12, 3189-3208.

  17. D. J. Foulis, R. J. Greechie, and M.K. Bennett, The Transition to Unigroups, International Journal of Theoretical Physics, 37 (1998), No. 1, 45-63.

  18. M. K. Bennett, D. J. Foulis, and R. J. Greechie, Quotients of Interval Effect Algebras, International Journal of Theoretical Physics, 35 (1996), No. 11, 2321-2338.

  19. D. J. Foulis, M.K. Bennett, and R. J. Greechie, Test Groups and Effect Algebras, International Journal of Theoretical Physics, 35 (1996), No. 6, 1117-1140.

  20. S. P. Gudder and R. J. Greechie, Effect Algebra Counterexamples, Mathematica Slovaca, 46 (1996), No. 4, 317-325.

  21. D. J. Foulis, R. J. Greechie, M. D. Chiara, and R. Giuntini, Quantum Logic, Encyclopedia of Applied Physics, 15 (1996), 229-255.

  22. R. J. Greechie and D. J. Foulis, The Transition to Effect Algebras, International Journal of Theoretical Physics, 34, No. 8, 1369-1382.

  23. R. J. Greechie, D. J. Foulis, and S. Pulmannová, The Center of an Effect Algebra, Order, 12 (1995), No. 1, 91-106.

  24. T. H. Choe, R. J. Greechie, and Y. Chae, Representations of Locally Compact Orthomodular Lattices, Topology and Îts Applications, 56 (1994), 165-173.

  25. D. J. Foulis, R. J. Greechie, and M.K. Bennett, Sums and Products of Interval Algebras, International Journal of Theoretical Physics, 33 (1994), No. 11, 2119-2136.

  26. D. J. Foulis, R. J. Greechie, and G. T. Rüttimann, Logicoalgebraic Structures II. Supports in Test Spaces, International Journal of Theoretical Physics, 32 (1993), No. 10, 1675-1690.

  27. T. H. Choe and R. J. Greechie, Profinite Orthomodular Lattices, Proceeding of The American Mathematical Society, 118 (1993), No. 4, 1053-1060.

  28. D. J. Foulis, R. J. Greechie, and G. T. Rüttimann, Filters and Supports in Orthoalgebras, International Journal of Theoretical Physics, 31 (1992), No. 5, 789-807.

  29. G. Bruns and R. J. Greechie, Blocks and Commutators in Orthomodular Lattices, Algebra Universalis, 27 (1990), No. 1, 1-9.

  30. G. Bruns, R. J. Greechie, J. Harding, and M. Roddy, Completions of Orthomodular Lattices, Order, 7 (1990), No. 1, 67-76.

  31. R. J. Greechie and L. Herman, Quasi-atoms in Symmetric Orthomodular Lattices, Algebra Universalis, 27 (1990), 455-465.

  32. G. Bruns, R. J. Greechie, and L. Herman, Orthomodular Lattice Containing MO2 as a Subalgebra, Journal of Pure and Applied Algebra, 68 (1990), 67-76.

  33. R. J. Greechie, Sites and Tours in Orthoalgebras and Orthomodular Lattices, Foundations of Physics, 20 (1990), No. 7, 915-923.

  34. H. Andréka, R. J. Greechie, and G. E. Strecker, On Residuated Approximations, in Categorical Methods in Computer Science, Lecture Notes in Computer Science, 393, Berlin, 1988, pp. 333-339.

  35. R. J. Greechie, Book Review, Foundations of Physics, 15 (1985), No. 2, 251-256

  36. R. J. Greechie and L. Herman, Commutator-Finite Orthomodular Lattices, Order (1985), 1, No. 3, 277-284.

  37. R. Godowski and R. J. Greechie, Some Equations Related to States on Orthomodular Lattices, Demonstratio Math, 17 (1984), 241-250.

  38. S. P. Gudder, G. T. Rüttimann, and R. J. Greechie, Measurements, Hilbert Space and Quantum Logics, Journal of Mathematical Physics, 23 (1982), No. 12, 2381-2386.

  39. G. Bruns and R. J. Greechie, Orthomodular Lattices Which Can be Covered by Finitely Many Blocks, Canadian Journal of Mathematics, 34 (1982), No. 3, 696-699.

  40. G. Bruns and R. J. Greechie, Some Finiteness Conditions For Orthomodular Lattices, Canadian Journal of Mathematics, 34 (1982), No. 3, 535-549.

  41. R. J. Greechie, A Non-Standard Quantum Logic With a Strong Set of States, in Current Issues in Quantum Logic, edited by E. G. Beltrametti and B. C. van Fraassen, Plenum Press, New York, 1981, pp. 375-380.

  42. R. J. Greechie, An Addendum to On Generating Distributive Sublattices of Orthomodular Lattices, Proceeding of The Americann Mathematical Society, 76 (1979), No. 2, 216-218.

  43. R. J. Greechie, Finite Groups As Automorphism Groups of Orthocomplemented Projective Planes, Journal of Australian Mathematical Society, Series A, 25 (1978), 19-24.

  44. R. J. Greechie, Another Nonstandard Quantum Logic (And How I Found It), in Mathematical Foundations of Quantum Theory (Papers from a conference held at Loyola University, New Orleans, June 2-4, 1977), edited by A. R. Marlow, Academic Press, New York, 1978, pp. 71-85.

  45. R. J. Greechie, On Generating Distributive Sublattices of Orthomodular Lattices, Proceeding of The American Mathematical Society, 67 (1977), No. 1, 17-22.

  46. R. J. Greechie, Any complete atomic orthomodular lattice with countably many atoms is a sublattice of one generated by three elements, Journal of Natrual Sciences and Mathematics, 17 (1977), 33-41.

  47. L. Haskins, S. P. Gudder, and R. J. Greechie, Perspectivity in Semimodular Orthomodular Posets, Journal of the London Mathematical Society, 9 (1975), 495-500.

  48. R. J. Greechie, Some Results From the Combinatorial Approach to Quantum Logic, Synthese, 29 (1974), 113-127.

  49. E. Gerelle, R. J. Greechie, and F. Miller, Weights on Spaces, in Physical Reality and Mathematical Description, E. Enz and J. Mehra, eds., Reidel, Dordrecht, 1974, pp. 169-192.

  50. R. J. Greechie and M. Ottenheimer, An Introduction to a Mathematical Approach to the Study of Kinship, P. Ballonoff, ed., Genealogical Mathematics, Paris and The Hague:Mouton, 1974, pp. 63-84.

  51. R. J. Greechie and S. P. Gudder, Quantum Logics, in: C.A. Hooker (ed.), Contemporary Research in the Foundations and Philosophy of Quantum Theory, Reidel, Dordrecht, 1973, pp. 143-173.

  52. L. M. Chawla and R. J. Greechie, On a Generalized Partial Order On Semigroups and Groups, Journal of Natrual Sciences and Mathematics, 12 (1972), No. 2, 389-396.

  53. R. J. Greechie, Orthomodular Lattices Admitting No States, Journal of Combinatorial Theory, Series A, 10 (1971), No. 2, 119-132.

  54. R. J. Greechie and S. P. Gudder, Is Quantum Logic a Logic, Helvetica Plrysica Acta, 44 (1971), 238-240.

  55. R. J. Greechie, Combinatorial Quantum Logic, Technical Report, No. 20, Department of Mathematics, Kansas State University, Manhattan, Kansas 1971.

  56. R. J. Greechie, A Remark on Adams' and Finch's Paper, Technical Report, No. 12, Department of Mathematics, Kansas State University, Manhattan, Kansas 1971.

  57. R. J. Greechie and F. R. Miller, On Structures Related to States on an Empirical Logic I. Weights on Finite Spaces, Technical Report, No. 16, Department of Mathematics, Kansas State University, Manhattan, Kansas 1970.

  58. R. J. Greechie, On Generating Pathological Orthomodular Structures, Technical Report, No. 13, Department of Mathematics, Kansas State University, Manhattan, Kansas 1970.

  59. R. J. Greechie, A Particular non-Atomistic Orthomodular Poset, Communications in Mathematical Physics, 14 (1969), No. 4, 326-328.

  60. R. J. Greechie, An Orthomodular Poset With a Full Set of States Not Embeddable in Hilbert Space, Carribean Journal of Science and Mathematics, 1 (1969), 15-26.

  61. R. J. Greechie, On the Structure of Orthomodular Lattices Satisfying the Chain Condition, Journal of Combinatorial Theory, 4 (1968), No. 3, 210-218.

  62. R. J. Greechie, Hyper-Irreducibility In an Orthomodular Lattice, Journal of Natrual Sciences and Mathematics, 8 (1968), No. 1, 109-111.

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