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On compactness and consistency in finite lattice-valued propositional logic

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Abstract
In this paper, we investigate the semantical theory of finite lattice-valued propositional logic based on finite lattice implication algebras. Based on the fuzzy set theory on a set of formulas, some propositions analogous to those in the classical logic are proved, and using the semantical consequence operation, the consistence and compactness is investigated.
Keywords
SYSTEMS, RESOLUTION PRINCIPLE, LF(X), FUZZY CLOSURE OPERATORS, Consistency, Fuzzy theory, Compactness, Lattice-valued logic, COMPLETENESS, Consequence operation

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MLA
Pan, XiaoDong, Yang Xu, Luis Martinez, et al. “On Compactness and Consistency in Finite Lattice-valued Propositional Logic.” Lecture Notes in Artificial Intelligence. Ed. Emilio Corchado, Manuel Graña Romay, & Alexandre Manhaes Savio. Vol. 6077. Berlin, Germany: Springer, 2010. 328–334. Print.
APA
Pan, X., Xu, Y., Martinez, L., Ruan, D., & Liu, J. (2010). On compactness and consistency in finite lattice-valued propositional logic. In Emilio Corchado, M. G. Romay, & A. M. Savio (Eds.), Lecture Notes in Artificial Intelligence (Vol. 6077, pp. 328–334). Presented at the 5th International conference on Hybrid Artificial Intelligence Systems (HAIS 2010), Berlin, Germany: Springer.
Chicago author-date
Pan, XiaoDong, Yang Xu, Luis Martinez, Da Ruan, and Jun Liu. 2010. “On Compactness and Consistency in Finite Lattice-valued Propositional Logic.” In Lecture Notes in Artificial Intelligence, ed. Emilio Corchado, Manuel Graña Romay, and Alexandre Manhaes Savio, 6077:328–334. Berlin, Germany: Springer.
Chicago author-date (all authors)
Pan, XiaoDong, Yang Xu, Luis Martinez, Da Ruan, and Jun Liu. 2010. “On Compactness and Consistency in Finite Lattice-valued Propositional Logic.” In Lecture Notes in Artificial Intelligence, ed. Emilio Corchado, Manuel Graña Romay, and Alexandre Manhaes Savio, 6077:328–334. Berlin, Germany: Springer.
Vancouver
1.
Pan X, Xu Y, Martinez L, Ruan D, Liu J. On compactness and consistency in finite lattice-valued propositional logic. In: Corchado E, Romay MG, Savio AM, editors. Lecture Notes in Artificial Intelligence. Berlin, Germany: Springer; 2010. p. 328–34.
IEEE
[1]
X. Pan, Y. Xu, L. Martinez, D. Ruan, and J. Liu, “On compactness and consistency in finite lattice-valued propositional logic,” in Lecture Notes in Artificial Intelligence, San Sebastián, Spain, 2010, vol. 6077, pp. 328–334.
@inproceedings{2918696,
  abstract     = {In this paper, we investigate the semantical theory of finite lattice-valued propositional logic based on finite lattice implication algebras. Based on the fuzzy set theory on a set of formulas, some propositions analogous to those in the classical logic are proved, and using the semantical consequence operation, the consistence and compactness is investigated.},
  author       = {Pan, XiaoDong and Xu, Yang and Martinez, Luis and Ruan, Da and Liu, Jun},
  booktitle    = {Lecture Notes in Artificial Intelligence},
  editor       = {Corchado, Emilio and Romay, Manuel Graña and Savio, Alexandre Manhaes},
  isbn         = {9783642138027},
  issn         = {0302-9743},
  keywords     = {SYSTEMS,RESOLUTION PRINCIPLE,LF(X),FUZZY CLOSURE OPERATORS,Consistency,Fuzzy theory,Compactness,Lattice-valued logic,COMPLETENESS,Consequence operation},
  language     = {eng},
  location     = {San Sebastián, Spain},
  pages        = {328--334},
  publisher    = {Springer},
  title        = {On compactness and consistency in finite lattice-valued propositional logic},
  url          = {http://dx.doi.org/10.1007/978-3-642-13803-4_41},
  volume       = {6077},
  year         = {2010},
}

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