PAL2v: Key points

How to use the PAL2v? What are the main algorithms?

1. Para-analyzer: Direct application of PAL2v, division of the lattice into small regions or logical states, used for decision making in expert systems;

2. ParaExtrCTX: Paraconsistent Extractor of Contradictions between multiple measurements of the same magnitude.

3. Average Extractor: learning cell network used to extract a moving average from a database.

4. Paraconsistent Analysis Network (PANnet): interconnection of several paraconsistent analysis nodes (PAN) and paraconsistent neural cells (PANC) for analysis, data processing, comparison and classification of patterns.

5. PAL2v filter: Network of learning cells (PANCL) or PANCLCTX) forming a low-pass (LPF) or high-pass (HPF) filter. The number of cascading cells determines the order of the filter.

6. Paraconsistent Neural Networks: (PNN): Paraconsistent analysis node (PAN) as a trainable neuron in a paraconsistent artificial neural network, with weights and bias at the synapses similar to that of classical artificial neural networks (ANNs). In the literature there are registered applications of feed-forward PNN and RPNN (recurrent paraconsistent neural network) for temporal sequences.

Paraconsistent Extractor of Contradiction

Arnaldo Carvalho (2023). Paraconsistent Extractor of Contradiction (ParaXctr). MATLAB Central File Exchange. Retrieved May 24, 2023.  

https://www.mathworks.com/matlabcentral/fileexchange/129784-paraconsistent-extractor-of-contradiction-paraxctr

Paraconsistent Artificial Neural Cells (PANC)

Arnaldo Carvalho (2023). Paraconsistent Artificial Neural Cells (PANC), MATLAB Central File Exchange. Retrieved May 24, 2023. 

https://www.mathworks.com/matlabcentral/fileexchange/129639-paraconsistent-artificial-neural-cells-panc

Pal2v Filter

Arnaldo Carvalho (2023). PAL2v Filter, MATLAB Central File Exchange. Retrieved May 24, 2023. 

https://www.mathworks.com/matlabcentral/fileexchange/129644-pal2v-filter

Paraconsistent Neural Network (PNN)

Arnaldo Carvalho (2023). Paraconsistent Neural Network (PNN). MATLAB Central File Exchange. Retrieved June 13, 2023. 

https://www.mathworks.com/matlabcentral/fileexchange/130739-paraconsistent-neural-network-pnn

Videos

• Espírito de Contradição (The Spirit of Contradiction) - Documentário Vida e Obra de Dr. Newton da Costa - 2017 (Portuguese):  https://youtu.be/8gKKabtLA_U?si=kisBYFhK4JBK3whn

• Ideias brasileiras - Newton da Costa e as lógicas paraconsistentes - Canal Ad Infinitum - 2022 (Portuguese): https://www.youtube.com/watch?v=gBqIujObO3g

• LPA2v Overview e Aplicações Labmax 09052023 (Portuguese): https://youtu.be/tITQF6CxBK8

• Identificação e Controle de Sistemas Dinâmicos com RNP (short, Portuguese) - 13/08/2021: https://youtu.be/vyVTAesaFTU

• Identificação e Controle de Sistemas Dinâmicos com RNP (X WMO  - 2021): https://youtu.be/_Opk0ufHYk8

• Rotary Inverted Pendulum (RIP) Identification for Control (I4C) by Paraconsistent Neural Network (PNN) (English): https://youtu.be/4NdneDqFfDE

Basic PAL2v Algorithm

References

[1] Arnaldo de Carvalho Junior, João Francisco Justo, Alexandre Maniçoba de Oliveira, João Inacio da Silva Filho, A comprehensive review on paraconsistent annotated evidential logic: Algorithms, Applications, and Perspectives, Engineering Applications of Artificial Intelligence, Volume 127, Part B, 2024, 107342, ISSN 0952-1976 DOI: 10.1016/j.engappai.2023.107342. https://www.sciencedirect.com/science/article/pii/S0952197623015269 

[2] A. De Carvalho Jr., B. A. Angelico, J. F. Justo, A. M. de Oliveira, J. I. Da Silva Filho, Model reference control by recurrent neural network built with paraconsistent neurons for trajectory tracking of a rotary inverted pendulum, Applied Soft Computing 133 (2023) 109927. DOI:10.1016/j.asoc.2022.109927. https://www.sciencedirect.com/science/article/abs/pii/S1568494622009760

[3] A. De Carvalho Jr., J. F. Justo, B. A. Angelico, A. M. De Oliveira, J. I. Da Silva Filho, Rotary inverted pendulum identification for control by paraconsistent neural network, IEEE Access 9 (2021) 74155–74167. DOI: 10.1109/ACCESS.2021.3080176. https://ieeexplore.ieee.org/document/9430548

[4] A. De Carvalho Jr., J. F. Justo, B. A. Angélico, et al. Paraconsistent State Estimator for a Furuta Pendulum Control. SN COMPUT. SCI. 4, 29 (2023). DOI: 10.1007/s42979-022-01427-z. https://link.springer.com/article/10.1007/s42979-022-01427-z

[5] A. De Carvalho, Jr., J. I. Da Silva Filho, M. C. Mario, M. F. Blos, and C. M. da Cruz, A Study of Paraconsistent Artificial Neural Cell of Learning Applied as PAL2v Filter, in IEEE Latin America Transactions, vol. 16, no. 1, pp. 202-209, Jan. 2018, DOI: 10.1109/TLA.2018.8291474. https://ieeexplore.ieee.org/document/8291474

[6] A. De Carvalho Jr., et al. Paraconsistent logic approach for active noise reduction. Journal of Mechatronic Engineering. 2020;3(1):2–8. DOI: 10.21439/jme.v3i1.81 . http://jme.ifce.edu.br/index.php/jme/article/view/81

[7] De Carvalho Jr., A. et al. (2023). A Paraconsistent Artificial Neural Cell of Learning by Contradiction Extraction (PANCLCTX) with Application Examples. In: Abe, J.M. (eds) Advances in Applied Logics . Intelligent Systems Reference Library, vol 243. Springer, Cham. DOI: 10.1007/978-3-031-35759-6_5.

[8] J. I. Da Silva Filho, Treatment of Uncertainties with Algorithms of the Paraconsistent Annotated Logic,  Journal of Intelligent Learning Systems and Applications, Vol. 4 No. 2, 2012, pp. 144-153. DOI: 10.4236/jilsa.2012.42014. https://www.scirp.org/journal/paperinformation.aspx?paperid=19263

[9] J. I. Da Silva Filho, G. Lambert-Torres, L. Ferrara, M. Mário, M. Santos, A. Onuki, J. Camargo and A. Rocco, Paraconsistent Algorithm Extractor of Contradiction Effects - Paraextrctr, Journal of Software Engineering and Applications, Vol. 4 No. 10, 2011, pp. 579-584. DOI: 10.4236/jsea.2011.410067. 

[10] M. S. Coelho, J. I. da Silva Filho, H. M. Côrtes, A. De Carvalho Jr., M. F. Blos, M. C. Mario, A. Rocco, Hybrid pi controller constructed with paraconsistent annotated logic, Control Engineering Practice 84 (2019) 112–124. DOI:10.1016/j.conengprac.2018.11.007. https://www.sciencedirect.com/science/article/abs/pii/S0967066118306932

[11] Da Silva Filho, J.I.; Fernandes, C.L.M.; Silveira, R.S.d.; Gomes, P.M.; Matos, S.L.d.C.; Santo, L.d.E.; Nunes, V.C.; Côrtes, H.M.; Lopes, W.A.C.; Mario, M.C.; Garcia, D.V.; Torres, C.R.; Abe, J.M.; Lambert-Torres, G. Process of Learning from Demonstration with Paraconsistent Artificial Neural Cells for Application in Linear Cartesian Robots. Robotics 2023, 12, 69. DOI: 10.3390/robotics12030069. https://www.mdpi.com/2218-6581/12/3/69

[12] M. S. Coelho, J. I. da Silva Filho, H. M. Côrtes, A. De Carvalho Jr., M. F. Blos, M. C. Mario, A. Rocco, Hybrid pi controller constructed with paraconsistent annotated logic, Control Engineering Practice 84 (2019) 112–124. DOI:10.1016/j.conengprac.2018.11.007. https://www.sciencedirect.com/science/article/abs/pii/S0967066118306932

[13] D. V. Garcia, J. I. Da Silva Filho, L. Silveira, M. T. T. Pacheco, J. M. Abe, A. De Carvalho Jr., M. F. Blos, C. A. G. Pasqualucci, M. C. Mario, Analysis of Raman spectroscopy data with algorithms based on paraconsistent logic for characterization of skin cancer lesions, Vibrational Spectroscopy 103 (2019) 1–10. DOI:10.1016/j.vibspec.2019.102929. https://www.sciencedirect.com/science/article/abs/pii/S092420311830345X

[14] Da Silva Filho, J. I.; Oliveira, R. A. B..; Rodrigues, M. C.; Côrtes, H. M.; Rocco, A.; Mario, M. C.; Garcia, D. V.; Abe, J. M.; Torres, C. R.; Ricciotti, V. B. D.; Ricciotti, A. C. D.; De Carvalho Jr., A.; Lambert-Torres, G. Predictive Controller Based on Paraconsistent Annotated Logic for Synchronous Generator Excitation Control, Energies 2023, 16(4), 1934; DOI: Energies 2023, 16(4), 1934. DOI: Energies 2023, 16(4), 1934; DOI: 10.3390/en16041934 . https://www.mdpi.com/1996-1073/16/4/1934.

[15] Rodrigues, M. C., Carvalho Junior, A. de ., Santos, A. R., Mario, M. C., Rosa, V. da S., Silva Filho, J. I. da ., Côrtes, H. M., Garcia, D. V., Giordano, F., & Lambert-Torres, G.. (2024). Paraconsistent Artificial Neural Network (PANnet) applied to the Detection of (NOx) Nitrogen Oxides Emissions in Petrochemical Combustion Systems. Brazilian Archives of Biology and Technology, 67, e24240601.. DOI: 10.1590/1678-4324-2024240601..https://www.scielo.br/j/babt/a/ccfsmztyN7KccY9Y6SrvmXR/?format=pdf&lang=en