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: Contribution to journal › Conference article › 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
Pages (from-to)	328-334
Number of pages	7
Journal	Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
Volume	6077 LNAI
Issue number	PART 2
DOIs	https://doi.org/10.1007/978-3-642-13803-4_41
Publication status	Published (in print/issue) - 2010
Event	5th International Conference on Hybrid Artificial Intelligence Systems, HAIS 2010 - San Sebastian, Spain Duration: 23 Jun 2010 → 25 Jun 2010

Keywords

Compactness
Consequence operation
Consistency
Fuzzy theory
Lattice-valued logic

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

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title = "On compactness and consistency in finite lattice-valued propositional logic",

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

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

year = "2010",

doi = "10.1007/978-3-642-13803-4\_41",

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volume = "6077 LNAI",

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journal = "Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)",

issn = "1611-3349",

publisher = "Springer Science and Business Media Deutschland GmbH",

number = "PART 2",

note = "5th International Conference on Hybrid Artificial Intelligence Systems, HAIS 2010 ; Conference date: 23-06-2010 Through 25-06-2010",

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On compactness and consistency in finite lattice-valued propositional logic. / Pan, Xiaodong; Xu, Yang; Martinez, Luis et al.
In: Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics), Vol. 6077 LNAI, No. PART 2, 2010, p. 328-334.

Research output: Contribution to journal › Conference article › peer-review

TY - JOUR

T1 - On compactness and consistency in finite lattice-valued propositional logic

AU - Pan, Xiaodong

AU - Xu, Yang

AU - Martinez, Luis

AU - Ruan, Da

AU - Liu, Jun

PY - 2010

Y1 - 2010

N2 - 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.

AB - 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.

KW - Compactness

KW - Consequence operation

KW - Consistency

KW - Fuzzy theory

KW - Lattice-valued logic

UR - https://www.scopus.com/pages/publications/77954567330

U2 - 10.1007/978-3-642-13803-4_41

DO - 10.1007/978-3-642-13803-4_41

M3 - Conference article

AN - SCOPUS:77954567330

SN - 1611-3349

VL - 6077 LNAI

SP - 328

EP - 334

JO - Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)

JF - Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)

IS - PART 2

T2 - 5th International Conference on Hybrid Artificial Intelligence Systems, HAIS 2010

Y2 - 23 June 2010 through 25 June 2010

ER -

On compactness and consistency in finite lattice-valued propositional logic

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Keywords

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