The B4-Modalized Propositional Logic

Cun Gen Cao; Yue Fei Sui; Shao Bo Deng

doi:10.4028/www.scientific.net/AMM.743.343

Paper Titles

A Novel Method for Segmenting and Ranking Nuclei for Cervical Cell
p.321

Two New Parallel Algorithms Based on QPSO
p.325

Comments on “A Novel Image Encryption-Compression Scheme Using Hyper-Chaos and Chinese Remainder Theorem”
p.333

Research on Multi-Distribution Center Location Based on Fruit Fly – Immune Algorithm
p.338

The B₄-Modalized Propositional Logic
p.343

Adaptive Detection Algorithm Research of Road Image Edge Line
p.347

An Improved ESPRIT Algorithm for Fast Frequency Estimation
p.351

System of HD Digital Audio Decoder
p.355

The Optimization of SIFT Feature Matching Algorithm on Face Recognition Based on BP Neural Network
p.359

HomeApplied Mechanics and MaterialsApplied Mechanics and Materials Vol. 743The B4-Modalized Propositional Logic

The B₄-Modalized Propositional Logic

Abstract:

A modalized propositional Belnap-Dunn logic will be proposed in this paper which thereare four modalities [t]; [T]; [⊥]; [f] to represent the four values t;T;⊥; f; respectively, and a Gentzentypeddeduction system will be given so that the the system is sound and complete with the four-valuedsemantics of the Belnap-Dunn logic.

You might also be interested in these eBooks

View Preview

Info:

Periodical:

Applied Mechanics and Materials (Volume 743)

Pages:

343-346

DOI:

https://doi.org/10.4028/www.scientific.net/AMM.743.343

Citation:

Cite this paper

Online since:

March 2015

Authors:

Cun Gen Cao*, Yue Fei Sui, Shao Bo Deng

Keywords:

Belnap-Dunn Logic, Completeness, Modality, Soundness

Export:

RIS, BibTeX

Price:

Permissions CCC:

Request Permissions

Permissions PLS:

Request Permissions

Сopyright:

Citation:

* - Corresponding Author

References

[1] N. Belnap (1977a): How a computer should think. In G. Ryle (edt. ), Contemporary Aspects of Philosophy, pages 30-56. Oriel Press, (1977).

Google Scholar

[2] N. Belnap (1977b): A useful four-valued logic. In J. M. Dunn and G. Epstein (eds. ), Modern Uses of Multiple-valued Logic, pages 8-37. D. Reidel.

DOI: 10.1007/978-94-010-1161-7_2

Google Scholar

[3] J. A. Bergstra and A. Ponse(1998): Kleene's three-valued logic and process algebra. Information Processing Letters, 67(2): 95-103.

DOI: 10.1016/s0020-0190(98)00083-0

Google Scholar

[4] J. M. Font (1997): Belnap's four-valued logic and De Morgan lattices. Logic Journal of the I.G.P.L., 5(3): 413-440.

Google Scholar

[5] W. Li (2010): Mathematical Logic, Foundations for Information Science, Progress in Computer Science and Applied Logic, vol. 25, Birkhäuser.

Google Scholar

[6] A. P. Pynko (1995b): Characterizing Belnap's logic via De Morgan's laws. Mathematical Logic Quarterly, 41(4): 442-454.

DOI: 10.1002/malq.19950410403

Google Scholar

[7] A. P. Pynko (1999): Implicational classes of De Morgan lattices. Discrete Math., 205(1-3): 171-181.

DOI: 10.1016/s0012-365x(99)00007-2

Google Scholar

[8] O. Rodrigues and A. Russo (1998): A translation method for Belnap logic. Imperial College RR DoC98/7.

Google Scholar