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Section A

Dedekind–MacNeille completion and Cartesian product of multi-adjoint lattices

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Pages 1742-1752 | Received 06 Oct 2011, Accepted 23 Apr 2012, Published online: 28 May 2012

References

  • Allwein , G. and Dunn , J. M. 1993 . Kripke models for linear logic . J. Symb. Logic. , 58 : 514 – 545 .
  • Almendros-Jiménez , J. , Luna , A. and Moreno , G. A Flexible XPath-based Query Language Implemented With Fuzzy Logic Programming . Proceedings of 5th International Symposium on Rules: Research Based, Industry Focused, RuleML’11, Lecture Notes on Computer Science 6826 . July 19–21 , Barcelona , Spain. pp. 186 – 193 . Berlin Heidelberg : Springer Verlag .
  • Caballero , R. , Rodríguez-Artalejo , M. and Romero-Díaz , C. A. Similarity-based Reasoning in Qualified Logic Programming . Proceedings of the 10th International ACM SIGPLAN Conference on Principles and Practice of Declarative Programming, PPDP ’08 . Valencia , Spain. pp. 185 – 194 . New York , , USA : ACM .
  • Cabrera , I. , Cordero , P. , Gutiérrez , G. , Martínez , J. and Ojeda-Aciego , M. 2010 . A coalgebraic approach to non-determinism: Applications to multilattices . Inf. Sci. , 180 : 4323 – 4335 .
  • Cabrera , I. , Cordero , P. , Gutiérrez , G. , Martínez , J. and Ojeda-Aciego , M. Coalgebras and Non-determinism: An Application to Multilattices . Proceedings of Physics and Computation . Luxor , Egypt.
  • Cabrera , I. P. , Cordero , P. and Ojeda-Aciego , M. 2011 . Non-deterministic algebraic structures for soft computing . Lect. Notes Comp. Sci. , 6692 : 437 – 444 .
  • Damásio , C. , Madrid , N. and Ojeda-Aciego , M. 2011 . On the notions of residuated-based coherence and bilattice-based consistence . Lect. Notes Comp. Sci. , 6857 : 115 – 122 .
  • Davey , B. and Priestley , H. 2002 . Introduction to Lattices and Order , 2 , Cambridge : Cambridge University Press .
  • Dedekind , R. 1872 . Stetigkeit und irrationale Zahlen , Braunscheweig : Friedrich Vieweg und Sohn .
  • Gehrke , M. and Harding , J. 2001 . Bounded lattice expansions . J. Algebra , 238 : 345 – 371 .
  • Gehrke , M. , Harding , J. and Venema , Y. 2005 . MacNeille completions and canonical extensions . Trans. Am. Math. Soc. , 358 : 573 – 590 .
  • Hartonas , C. 1997 . Duality for lattice-ordered algebras and for normal algebraizable logics . Estudia Logica , 58 : 403 – 450 .
  • Jonnson , B. and Tarski , A. 1951 . Boolean algebras with operators I . Am. J. Math. , 73 : 891 – 939 .
  • Julián , P. , Moreno , G. and Penabad , J. On the Declarative Semantics of Multi-adjoint Logic Programs . Proceedings of the 10th International Work-Conference on Artificial Neural Networks, IWANN’09, Salamanca, Lecture Notes on Computer Science 5517 . pp. 253 – 260 . Berlin : Springer .
  • Lloyd , J. 1987 . Foundations of Logic Programming , Berlin : Springer-Verlag .
  • MacCaull , W. 1996 . Kripke semantics for logics with bck implication . Bull. Sect. Logic (University of Lódź) , 25 : 41 – 51 .
  • MacNeille , H. M. 1937 . Partially ordered sets . Trans. Am. Math. Soc. , 42 : 416 – 460 .
  • Medina , J. and Ojeda-Aciego , M. Towards Attribute Reduction in Multi-adjoint Concept Lattices . Proceedings of Concept Lattices and Applications, CLA’10 . pp. 92 – 103 . Sevilla , , Spain
  • Medina , J. , Ojeda-Aciego , M. and Ruiz-Calviño , J. 2007 . Fuzzy logic programming via multilattices . Fuzzy Set. Syst. , 158 : 674 – 688 .
  • Medina , J. , Ojeda-Aciego , M. and Ruiz-Calviño , J. 2007 . On reachability of minimal models of multilattice-based logic programming . LNAI , 4827 : 271 – 282 .
  • Medina , J. , Ojeda-Aciego , M. and Ruiz-Calviño , J. 2009 . Formal concept analysis via multi-adjoint concept lattices . Fuzzy Set. Syst. , 160 : 130 – 144 .
  • Medina , J. , Ojeda-Aciego , M. and Vojtáš , P. Multi-adjoint Logic Programming With Continuous Semantics . Proceedings of Logic Programming and Non-monotonic Reasoning, LPNMR’01 . Viena , Austria. pp. 351 – 364 . Berlin Heidelberg : Springer . LNAI 2173
  • Medina , J. , Ojeda-Aciego , M. and Vojtáš , P. A Procedural Semantics for Multi-adjoint Logic Programing . Porto , Portugal. pp. 290 – 297 . Berlin Heidelberg : Springer-Verlag . LNAI 2258
  • Medina , J. , Ojeda-Aciego , M. and Vojtáš , P. 2004 . Similarity-based Unification: A multi-adjoint approach . Fuzzy Set. Syst. , 146 : 43 – 62 .
  • Morcillo , P. , Moreno , G. , Penabad , J. and Vázquez , C. A Practical Management of Fuzzy Truth Degrees Using FLOPER . Proceedings of 4th International Symposium on Rule Interchange and Applications, RuleML’10 . October 21–23 , Washington, DC . pp. 119 – 126 . Berlin Heidelberg : Springer Verlag . Lecture Notes on Computer Science 6403
  • Morcillo , P. , Moreno , G. , Penabad , J. and Vázquez , C. Fuzzy Computed Answers Collecting Proof Information . Advances in Computational Intelligence. Proceedings of the 11th International Work-Conference on Artificial Neural Networks, IWANN’11 . Torremolinos , Spain. pp. 445 – 452 . Berlin Heidelberg : Springer Verlag . Lecture Notes on Computer Science 6692
  • Nguyen , H. T. and Walker , E. 2006 . A First Course in Fuzzy Logic , 3 , Boca Ratón , FL : Chapman & Hall/CRC .
  • Rodríguez-Artalejo , M. and Romero-Díaz , C. A. 2008 . A declarative semantics for clp with qualification and proximity . Theory Pract. Logic Prog. , 10 : 627 – 642 .
  • Rodríguez-Artalejo , M. and Romero-Díaz , C. A. Quantitative Logic Programming Revisited . Functional and Logic Programming (FLOPS’08) . Ise , Japan. pp. 272 – 288 . Berlin Heidelberg : Springer . Lecture Notes on Computer Science 4989
  • Rodríguez-Artalejo , M. and Romero-Díaz , C. A. 2009 . Qualified logic programming with bivalued predicates . Electronic Notes Theor. Comput. Sci. , 248 : 67 – 82 .
  • Voutsadakis , G. 2007 . Dedekind–Macneille Completion of n-ordered Sets . Order , 24 : 15 – 29 .

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