D-posets. (English) Zbl 0789.03048

Summary: This paper deals with partially ordered sets for which a difference (as a partial binary operation) is introduced. These structures, so-called \(D\)- posets, are a natural generalization of quantum logics, real vector lattices, orthoalgebras, MV algebras. At the same time they give a new look at fuzzy quantum logics.


03G12 Quantum logic
81P10 Logical foundations of quantum mechanics; quantum logic (quantum-theoretic aspects)
06A06 Partial orders, general
Full Text: EuDML


[1] CHOVANEC F.: Compatibility problem in quasi-orthocomplemented posets. Math. Slovaca 43 (1993), 89-103. · Zbl 0776.06006
[2] CHOVANEC F., JUREČKOVÁ M.: Law of large numbers in D-posets of fuzzy sets. Tatra Mountains Math. Publ. 1 (1992), 15-18. · Zbl 0795.03095
[3] DVUREČENSKIJ A.: Gleason’s Theorem and Its Applications. Kluwer Acad. Publ., Dordrecht-Boston-London, 1993. · Zbl 0795.46045
[4] DVUREČENSKIJ A., KÔPKA F.: On representation theorems for observables in weakly complemented posets. Demonstratio Math. 33 (1990), 911-920. · Zbl 0767.03032
[5] DVUREČENSKIJ A., TIRPÁKOVÁ A.: Sum of observables in fuzzy quantum spaces. Appl. Math. 37 (1992), 40-50. · Zbl 0753.60005
[6] FOULIS D. J.: Coupled physical systems. Found. Phys. 19 (1989), 905-922.
[7] KÔPKA F.: D-posets of fuzzy sets. Tatra Mountains Math. Publ. 1 (1992), 83-87. · Zbl 0797.04011
[8] MESIAR R.: Fuzzy logics and observables. Internat. J. Theoret. Phys. 32 (1993), 1143-1151. · Zbl 0791.03038 · doi:10.1007/BF00671795
[9] MESIAR R.: h-fuzzy quantum logics. Found. Phys. · Zbl 0819.03049 · doi:10.1007/BF00670686
[10] MUNDICI D.: Interpretation of AF C*-algebras in Lukasiewicz sentential calculus. J. Funct. Anal. 65 (1986), 15-53. · Zbl 0597.46059 · doi:10.1016/0022-1236(86)90015-7
[11] NAVARA M., PTÁK P.: Difference posets and orthoalgebras. · Zbl 0691.03045
[12] PTÁK P., PULMANNOVÁ S.: Orthomodular Structures as Quantum Logics. VEDA and Kluwer Acad. PubL, Bratislava and Dordrecht, 1991. · Zbl 0743.03039
[13] PYKACZ J.: Quantum logics and soft fuzzy probability spaces. BUSEFAL 32 (1987), 150-157. · Zbl 0662.03055
[14] RIEČAN B.: A new approach to some notions of statistical quantum mechanics. BUSEFAL 35 (1988), 4-6.
[15] VARADARAJAN V. S.: Geometry of Quantum Theory. Van Nostrand. New York, 1968. · Zbl 0155.56802
[16] WEBER S.: Two integrals and some modified version-critical remarks. Fuzzy Sets and Systems 20 (1986), 97-105. · Zbl 0595.28012 · doi:10.1016/S0165-0114(86)80035-5
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.