On compactness and consistency in finite lattice-valued propositional logic

Xiaodong Pan; Yang Xu; Luis Martinez; Da Ruan; Jun Liu

doi:10.1007/978-3-642-13803-4_41

On compactness and consistency in finite lattice-valued propositional logic

Xiaodong Pan, Yang Xu, Luis Martinez, Da Ruan, Jun Liu

Research output › peer-review

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.

Original language	English
Title of host publication	Hybrid Artificial Intelligence Systems
Place of Publication	Heidelberg, Germany
Pages	328-334
Number of pages	7
Volume	6077 LNAI
Edition	PART 2
DOIs	https://doi.org/10.1007/978-3-642-13803-4_41
State	Published - 2010
Event	HAIS - 2010: 5th International Conference on Hybrid Artificial Intelligence Systems - 5th International Conference HAIS2010, San Sebastian Duration: 23 Jun 2010 → 25 Jun 2010

Publication series

Name	Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
Volume	6077
ISSN (Print)	0302-9743

Conference

Conference	HAIS - 2010
Abbreviated title	HAIS
Country/Territory	Spain
City	San Sebastian
Period	2010-06-23 → 2010-06-25

ASJC Scopus subject areas

Theoretical Computer Science
General Computer Science

Access to Document

10.1007/978-3-642-13803-4_41License: Unspecified

Cite this

Pan, X., Xu, Y., Martinez, L., Ruan, D., & Liu, J. (2010). On compactness and consistency in finite lattice-valued propositional logic. In Hybrid Artificial Intelligence Systems (PART 2 ed., Vol. 6077 LNAI, pp. 328-334). (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics); Vol. 6077).. https://doi.org/10.1007/978-3-642-13803-4_41

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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 = "Lattice-valued logic, Consequence operation, Compactness, Fuzzy theory, Consistency",

author = "Xiaodong Pan and Yang Xu and Luis Martinez and Da Ruan and Jun Liu",

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Pan, X, Xu, Y, Martinez, L, Ruan, D & Liu, J 2010, On compactness and consistency in finite lattice-valued propositional logic. in Hybrid Artificial Intelligence Systems. PART 2 edn, vol. 6077 LNAI, Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics), vol. 6077, Heidelberg, Germany, pp. 328-334, HAIS - 2010, San Sebastian, Spain, 2010-06-23. https://doi.org/10.1007/978-3-642-13803-4_41

On compactness and consistency in finite lattice-valued propositional logic. / Pan, Xiaodong; Xu, Yang; Martinez, Luis et al.
Hybrid Artificial Intelligence Systems. Vol. 6077 LNAI PART 2. ed. Heidelberg, Germany, 2010. p. 328-334 (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics); Vol. 6077).

Research output › peer-review

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KW - Consequence operation

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Pan X, Xu Y, Martinez L, Ruan D, Liu J. On compactness and consistency in finite lattice-valued propositional logic. In Hybrid Artificial Intelligence Systems. PART 2 ed. Vol. 6077 LNAI. Heidelberg, Germany. 2010. p. 328-334. (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)). doi: 10.1007/978-3-642-13803-4_41