Graphic representation of MV-algebra pastings

We deal with a construction of some difference posets via a method of a pasting of MV-algebras. We generalize Greechie diagrams used in MV-algebra pastings. We give necessary and sufficient conditions under which the resulting pasting of an admissible system MV-algebras is a lattice-ordered D-poset.

[1]  State spaces of orthomodular structures , 2000 .

[2]  J. Møller,et al.  Statistical Inference and Simulation for Spatial Point Processes , 2003 .

[3]  Larry G. Epstein,et al.  Subjective Probabilities on Subjectively Unambiguous Events , 2001 .

[4]  Mirko Navara,et al.  The Pasting Constructions for Orthomodular Posets , 1991 .

[5]  C. Muresan The Reticulation of a Residuated Lattice , 2008 .

[6]  Petr Hájek,et al.  Metamathematics of Fuzzy Logic , 1998, Trends in Logic.

[7]  Pavel Pták,et al.  Orthocomplemented difference lattices with few generators , 2011, Kybernetika.

[8]  Petr Hájek,et al.  On witnessed models in fuzzy logic , 2007, Math. Log. Q..

[9]  Zdenka Riecanová Modular atomic effect algebras and the existence of subadditive states , 2004, Kybernetika.

[10]  Ferdinand Chovanec,et al.  Conditional states and independence in D-posets , 2010, Soft Comput..

[11]  L. P. Belluce Semisimple Algebras of Infinite Valued Logic and Bold Fuzzy Set Theory , 1986, Canadian Journal of Mathematics.

[12]  Jan Paseka Modularity, Atomicity and States in Archimedean Lattice Effect Algebras ? , 2010, 1001.1322.

[13]  Mi-Mi Kim,et al.  A NOTE ON SYMMETRIC DIFFERENCES OF ORTHOMODULAR LATTICES , 2003 .

[14]  K. Reidemeister,et al.  Topologische Fragen der Differentialgeometrie. V. Gewebe und Gruppen , 1929 .

[15]  Gejza Jenča The block structure of complete lattice ordered effect algebras , 2007, Journal of the Australian Mathematical Society.

[16]  Claudia Muresan,et al.  Characterization of the Reticulation of a Residuated Lattice , 2010, J. Multiple Valued Log. Soft Comput..

[17]  Laurentiu Leustean,et al.  The prime and maximal spectra and the reticulation of BL-algebras , 2003 .

[18]  Mária Jurečková,et al.  MV-Algebra Pasting , 2003 .

[19]  Mirko Navara Constructions of quantum structures , 2007 .

[20]  David J. Foulis,et al.  Filters and supports in orthoalgebras , 1992 .

[21]  Zdenka Riečanová Proper Effect Algebras Admitting No States , 2001 .

[22]  Claudia Murecsan Further Functorial Properties of the Reticulation , 2009, 0902.2264.

[23]  M. F.,et al.  Bibliography , 1985, Experimental Gerontology.

[24]  Petr Hájek,et al.  Complexity Issues in Axiomatic Extensions of Lukasiewicz Logic , 2009, J. Log. Comput..

[25]  Katerina Helisova,et al.  Power diagrams and interaction processes for unions of discs , 2008, Advances in Applied Probability.

[26]  Tomás Kroupa,et al.  Core of Coalition Games on MV-algebras , 2011, J. Log. Comput..

[27]  Jan Paseka,et al.  The inheritance of BDE-property in sharply dominating lattice effect algebras and (o)-continuous states , 2011, Soft Comput..

[28]  Gerhard Dorfer Noncommutative Symmetric Differences in Orthomodular Lattices , 2002 .

[29]  Josef Tkadlec,et al.  Greechie diagrams, nonexistence of measures in quantum logics, and Kochen–Specker‐type constructions , 1996 .

[30]  Richard J. Greechie,et al.  Orthomodular Lattices Admitting No States , 1971 .

[31]  David J. Foulis,et al.  Effects, Observables, States, and Symmetries in Physics , 2007 .

[32]  Sylvia Pulmannová,et al.  Orthomodular structures as quantum logics , 1991 .

[33]  For n ≥ 5 There Is No Nontrivial Z2-Measure on L(Rn) , 2004 .

[34]  Zdenka Riečanová Pastings of MV-Effect Algebras , 2004 .

[35]  C. Chang,et al.  Algebraic analysis of many valued logics , 1958 .

[36]  Wilhelm Blaschke,et al.  Geometrie der Gewebe : topologische Fragen der Differentialgeometrie , 1938 .

[37]  Daniele Mundici,et al.  Faithful and Invariant Conditional Probability in Łukasiewicz Logic , 2009, Towards Mathematical Philosophy.

[38]  Pavel Pták,et al.  Symmetric difference on orthomodular lattices and $Z_2$-valued states , 2009 .

[39]  Markus Dichtl Astroids and pastings , 1984 .

[40]  Pavel Pták,et al.  Orthocomplemented Posets with a Symmetric Difference , 2009, Order.

[41]  Gejza Jenvca Blocks of homogeneous effect algebras , 2001, Bulletin of the Australian Mathematical Society.

[42]  Franco Montagna,et al.  A logical and algebraic treatment of conditional probability , 2005, Arch. Math. Log..

[44]  Zdenka Riečanová,et al.  Generalization of Blocks for D-Lattices and Lattice-Ordered Effect Algebras , 2000 .

[45]  Roberto Cignoli,et al.  Free algebras in varieties of Stonean residuated lattices , 2007, Soft Comput..

[46]  Tomás Kroupa Many-dimensional observables on Łukasiewicz tribe: constructions, conditioning and conditional independence , 2005, Kybernetika.

[47]  L. P. Bellue Spectral spacess and non-commutative rings , 1991 .

[48]  Dov M. Gabbay,et al.  Handbook of Quantum Logic and Quantum Structures: Quantum Structures , 2007 .

[49]  D. Foulis,et al.  Effect algebras and unsharp quantum logics , 1994 .

[50]  Yongjian Xie,et al.  The pasting constructions of lattice ordered effect algebras , 2010, Inf. Sci..

[51]  Milan Matoušek Orthocomplemented lattices with a symmetric difference , 2009 .

[52]  Pavel Pták,et al.  On identities in orthocomplemented difference lattices , 2010 .

[53]  Sylvia Pulmannová,et al.  New trends in quantum structures , 2000 .