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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.

- J. Su, W. Feng, R. J. Greechie, Distributivity Conditions and the Order-Skeleton of a Lattice, Submitted to Algebra Universallis
- W. Feng, J. Su, R. J. Greechie, On Calculating Residuated Approximations, Submitted to Algebra Universallis
- K. J. Al-Agha and R. J. Greechie, Order Dimension of Orthomodular Amalgamations Over Trees,
*Order*,**25**(2008), No. 1, 55-68. - J. C. Carréga and R. J. Greechie, Coverings of [MOn] and Minimal Orthomodular Lattices,
*Algebra Universalis*,**58**(2008), No. 4, 427-459. - 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. - 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. - R. J. Greechie and B. J. Legan, Three Classes of Orthomodular Lattices,
*International Journal of Theoretical Physics*,**45**(2006), No. 2, 351-357. - 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. - 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. - D. J. Foulis and R. J. Greechie, Semisimplicial Unital Groups,
*International Journal of Theoretical Physics*,**43**(2004), 1689-1704. - 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. - S. P. Gudder and R. J. Greechie, Sequential Products on Effect Algebras,
*Reports on Mathematical Physics*,**49**(2002), No. 1, 87-111. - K. J. Al-Agha and R. J. Greechie, The Involutory Dimension of Involution Posets,
*Order*,**18**(2001), No. 4, 323-337. - D. J. Foulis and R. J. Greechie, Specification of Finite Effect Algebras,
*International Journal of Theoretical Physics*,**39**(2000), No. 3, 665-676. - 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. - 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. - 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. - 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. - 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. - S. P. Gudder and R. J. Greechie, Effect Algebra Counterexamples,
*Mathematica Slovaca*,**46**(1996), No. 4, 317-325. - D. J. Foulis, R. J. Greechie, M. D. Chiara, and R. Giuntini, Quantum Logic,
*Encyclopedia of Applied Physics*,**15**(1996), 229-255. - R. J. Greechie and D. J. Foulis, The Transition to Effect Algebras,
*International Journal of Theoretical Physics*,**34**, No. 8, 1369-1382. - R. J. Greechie, D. J. Foulis, and S. Pulmannová, The Center of an Effect Algebra,
*Order*,**12**(1995), No. 1, 91-106. - T. H. Choe, R. J. Greechie, and Y. Chae, Representations of Locally Compact Orthomodular Lattices,
*Topology and Îts Applications*,**56**(1994), 165-173. - 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. - 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. - T. H. Choe and R. J. Greechie, Profinite Orthomodular Lattices,
*Proceeding of The American Mathematical Society*,**118**(1993), No. 4, 1053-1060. - 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. - G. Bruns and R. J. Greechie, Blocks and Commutators in Orthomodular Lattices,
*Algebra Universalis*,**27**(1990), No. 1, 1-9. - G. Bruns, R. J. Greechie, J. Harding, and M. Roddy, Completions of Orthomodular Lattices,
*Order*,**7**(1990), No. 1, 67-76. - R. J. Greechie and L. Herman, Quasi-atoms in Symmetric Orthomodular Lattices,
*Algebra Universalis*,**27**(1990), 455-465. - 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. - R. J. Greechie, Sites and Tours in Orthoalgebras and Orthomodular Lattices,
*Foundations of Physics*,**20**(1990), No. 7, 915-923. - 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. - R. J. Greechie, Book Review,
*Foundations of Physics*,**15**(1985), No. 2, 251-256 - R. J. Greechie and L. Herman, Commutator-Finite Orthomodular Lattices,
*Order*(1985),**1**, No. 3, 277-284. - R. Godowski and R. J. Greechie, Some Equations Related to States on Orthomodular Lattices,
*Demonstratio Math*,**17**(1984), 241-250. - 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. - 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. - G. Bruns and R. J. Greechie, Some Finiteness Conditions For Orthomodular Lattices,
*Canadian Journal of Mathematics*,**34**(1982), No. 3, 535-549. - 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. - 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. - R. J. Greechie, Finite Groups As Automorphism Groups of Orthocomplemented Projective Planes,
*Journal of Australian Mathematical Society, Series A*,**25**(1978), 19-24. - 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. - R. J. Greechie, On Generating Distributive Sublattices of Orthomodular Lattices,
*Proceeding of The American Mathematical Society*,**67**(1977), No. 1, 17-22. - 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. - L. Haskins, S. P. Gudder, and R. J. Greechie, Perspectivity in Semimodular Orthomodular Posets,
*Journal of the London Mathematical Society*,**9**(1975), 495-500. - R. J. Greechie, Some Results From the Combinatorial Approach to Quantum Logic,
*Synthese*,**29**(1974), 113-127. - 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. - 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. - 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. - 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. - R. J. Greechie, Orthomodular Lattices Admitting No States,
*Journal of Combinatorial Theory, Series A*,**10**(1971), No. 2, 119-132. - R. J. Greechie and S. P. Gudder, Is Quantum Logic a Logic,
*Helvetica Plrysica Acta*,**44**(1971), 238-240. - R. J. Greechie, Combinatorial Quantum Logic,
*Technical Report*, No. 20, Department of Mathematics, Kansas State University, Manhattan, Kansas 1971. - R. J. Greechie, A Remark on Adams' and Finch's Paper,
*Technical Report*, No. 12, Department of Mathematics, Kansas State University, Manhattan, Kansas 1971. - 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. - R. J. Greechie, On Generating Pathological Orthomodular Structures,
*Technical Report*, No. 13, Department of Mathematics, Kansas State University, Manhattan, Kansas 1970. - R. J. Greechie, A Particular non-Atomistic Orthomodular Poset,
*Communications in Mathematical Physics*,**14**(1969), No. 4, 326-328. - 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. - R. J. Greechie, On the Structure of Orthomodular Lattices Satisfying the Chain Condition,
*Journal of Combinatorial Theory*,**4**(1968), No. 3, 210-218. - R. J. Greechie, Hyper-Irreducibility In an Orthomodular Lattice,
*Journal of Natrual Sciences and Mathematics*,**8**(1968), No. 1, 109-111.