Analysis of Physical Systems with Paraconsistent Annotated Logic: Introducing the Paraquantum Gamma Factor γ_{ψ}

Author(s)
João Inácio Da Silva Filho

ABSTRACT

In this paper we use a non-classical logic called ParaQuantum Logic (PQL) which is based on the foundations of the Paraconsistent Annotated logic with annotation of two values (PAL2v). The formalizations of the PQL concepts, which is represented by a lattice with four vertices, leads us to consider Paraquantum logical states ψ which are propagated by means of variations of the evidence Degrees extracted from measurements performed on the Observable Variables of the physical world. In this work we introduce the Paraquantum Gamma Factor γ_{Pψ} which is an expansion factor on the PQL lattice that act in the physical world and is correlated with the Paraquantum Factor of quantization h_{ψ} whose value is associated with a special logical state on the lattice which is identified with the Planck constant h. Our studies show that the behavior of the Paraquantum Gamma Factor γ_{Pψ}, at the time of reading the evidence Degrees through measurements of the Observable Variables in the physical world, is identical to that one of the Lorentz Factor γ used in the relativity theory. In the final part of this paper we present results about studies of expansion and contraction of the Paraquantum Logical Model which correlate the factors γ_{Pψ}, and γ. By applying these correlation factors, the lattice of the PQL suitable for the universe understudy can be contracted or expanded, allowing the quantization model to cover the several study fields of physics.

In this paper we use a non-classical logic called ParaQuantum Logic (PQL) which is based on the foundations of the Paraconsistent Annotated logic with annotation of two values (PAL2v). The formalizations of the PQL concepts, which is represented by a lattice with four vertices, leads us to consider Paraquantum logical states ψ which are propagated by means of variations of the evidence Degrees extracted from measurements performed on the Observable Variables of the physical world. In this work we introduce the Paraquantum Gamma Factor γ

KEYWORDS

Paraconsistent Logic, Paraquantum Logic, Classical Physic, Relativity Theory, Quantum Mechanics

Paraconsistent Logic, Paraquantum Logic, Classical Physic, Relativity Theory, Quantum Mechanics

Cite this paper

nullJ. Filho, "Analysis of Physical Systems with Paraconsistent Annotated Logic: Introducing the Paraquantum Gamma Factor γ_{ψ}," *Journal of Modern Physics*, Vol. 2 No. 12, 2011, pp. 1455-1469. doi: 10.4236/jmp.2011.212180.

nullJ. Filho, "Analysis of Physical Systems with Paraconsistent Annotated Logic: Introducing the Paraquantum Gamma Factor γ

References

[1] N. C. A. Da Costa and D. Marconi, “An Overview of Para- consistent Logic in the 80’s,” The Journal of Non- Classical Logic, Vol. 6, No. 1, 1989, pp. 5-32.

[2] D. Krause and O, Bueno, “Scientific Theories, Models, and the Semantic Approach,” Principia, NEL—Episte- mology and Logic Research Group, Federal University of Santa Catarina (UFSC), Santa Catarina, 2007, pp. 187- 201.

[3] N. C. A. Da Costa, V. S. Subrahmanian and C. Vago, “The Paraconsistent Logic PJ,” Mathematical Logic Quar- terly, Vol. 37, No. 9-12, 1991, pp. 139-148. doi:10.1002/malq.19910370903

[4] J. I. Da Silva Fiho, G. Lambert-Torres and J. M. Abe, “Uncertainty Treatment Using Paraconsistent Logic: Introducing Paraconsistent Artificial Neural Networks,” IOS Press, Amsterdam, 2010, p. 328.

[5] J. I. Da Silva Filho, A. Rocco, A. S. Onuki, L. F. P. Fer- rara and J. M. Camargo, “Electric Power Systems Con- tingencies Analysis by Paraconsistent Logic Applica- tion,” International Conference on Intelligent Systems Applications to Power Systems, Toki Messe, 5-8 November 2007, pp. 1-6. doi:10.1109/ISAP.2007.4441603

[6] J. I. Da Silva Filho, A. Rocco, M. C. Mario and L. F. P. Ferrara, “PES-Paraconsistent Expert System: A Computational Program for Support in Re-Establishment of the Electric Transmission Systems,” Proceedings of VI Congress of Logic Applied to Technology, Santos, 21-23 November 2007, p. 217.

[7] J. I. Da Silva Filho, A. Rocco, M. C. Mario and L. F. P. Ferrara, “Annotated Paraconsistent Logic Applied to an Expert System Dedicated for Supporting in an Electric Power Transmission Systems Re-Establishment,” 2006 IEEE PES on Power Systems Conference and Exposition, Atlanta, October 29 2006-November 1 2006, pp. 2212- 2220.

[8] P. A. Tipler and A. Llewellyn, “Modern Physics,” 5th Edition, W. H. Freeman and Company, New York, 2007.

[9] J. M. Abe and J. I. Da Silva Filho, “Inconsistency and Electronic Circuits,” In: E. Alpaydin, Ed., Proceedings of EIS’98 International ICSC Symposium on Engineering of Intelligent Systems, Vol. 3, 1998, pp. 191-197.

[10] N. C. A. Da Costa, “On the Theory of Inconsistent Formal Systems,” Notre Dame Journal of Formal Logic, Vol. 15, No. 4, 1974, pp. 497-510. doi:10.1305/ndjfl/1093891487

[11] J. I. Da Silva Filho and A. Rocco, “Power Systems Outage Possibilities Analysis by Paraconsistent Logic,” 2008 IEEE Power and Energy Society General Meeting: Conversion and Delivery of Electrical Energy in the 21st Century, Pittsburgh, 20-24 July 2008, pp. 1-6.

[12] D. Kleppner and R. K. Binding: “An Introduction to Mechanics” Mcgraw-Hill, Columbus, 1973, p. 600.

[13] P. A. Tipler, “Physics,” Worth Publishers, Inc., New York, 1976.

[14] P. A Tipler and G. M. Tosca, “Physics for Scientists,” 6th Edition, W. H. Freeman and Company, 2007.

[15] J. Bernstein, P. M. Fishbane and S. G. Gasiorowicz “Modern Physics,” Prentice-Hall, New York, 2000, p. 624.

[16] J. P. Mckelvey and H. Grotch “Physics for Science and Engineering,” Harper and Row Publisher Inc., New York, 1978, p. 426.

[17] M. Ference Jr., H. B. Lemon and R. J. Stephenson “Analytical Experimental Physics,” 2nd Editon, University of Chicago Press, Chicago, 1956.

[18] J. A. Wheeler and H. Z. Wojciech (eds), “Quantum Theory and Measurement,” Princeton University Press, Princeton, 1983.

[19] H. A. Blair and V. S. Subrahmanian, “Paraconsistent Lo- gic Programming,” 7th Conference on Foundations of Software Technology and Theoretical Computer Science, Pune, 17-19 December 1987.

[20] N. C. A. da Costa, D. Krause and O. Bueno, “Paraconsistent Logics and Paraconsistency,” In: D. Jacquette, D. M. Gabbay, P. Thagard and J. Woods, Eds., Philosophy of Logic, Elsevier, Series Handbook of the Philosophy of Science, Vol. 5, 2006, pp. 655-781.

[21] H. Reichenbach, “Philosophic Foundations of Quantum Mechanics,” University of California Press, Berkeley, 1944.

[22] F. Gross, “Relativistic Quantum Mechanics and Field Theory,” John Wiley & Sons, Inc., Hoboken, 1993, p. 97.

[1] N. C. A. Da Costa and D. Marconi, “An Overview of Para- consistent Logic in the 80’s,” The Journal of Non- Classical Logic, Vol. 6, No. 1, 1989, pp. 5-32.

[2] D. Krause and O, Bueno, “Scientific Theories, Models, and the Semantic Approach,” Principia, NEL—Episte- mology and Logic Research Group, Federal University of Santa Catarina (UFSC), Santa Catarina, 2007, pp. 187- 201.

[3] N. C. A. Da Costa, V. S. Subrahmanian and C. Vago, “The Paraconsistent Logic PJ,” Mathematical Logic Quar- terly, Vol. 37, No. 9-12, 1991, pp. 139-148. doi:10.1002/malq.19910370903

[4] J. I. Da Silva Fiho, G. Lambert-Torres and J. M. Abe, “Uncertainty Treatment Using Paraconsistent Logic: Introducing Paraconsistent Artificial Neural Networks,” IOS Press, Amsterdam, 2010, p. 328.

[5] J. I. Da Silva Filho, A. Rocco, A. S. Onuki, L. F. P. Fer- rara and J. M. Camargo, “Electric Power Systems Con- tingencies Analysis by Paraconsistent Logic Applica- tion,” International Conference on Intelligent Systems Applications to Power Systems, Toki Messe, 5-8 November 2007, pp. 1-6. doi:10.1109/ISAP.2007.4441603

[6] J. I. Da Silva Filho, A. Rocco, M. C. Mario and L. F. P. Ferrara, “PES-Paraconsistent Expert System: A Computational Program for Support in Re-Establishment of the Electric Transmission Systems,” Proceedings of VI Congress of Logic Applied to Technology, Santos, 21-23 November 2007, p. 217.

[7] J. I. Da Silva Filho, A. Rocco, M. C. Mario and L. F. P. Ferrara, “Annotated Paraconsistent Logic Applied to an Expert System Dedicated for Supporting in an Electric Power Transmission Systems Re-Establishment,” 2006 IEEE PES on Power Systems Conference and Exposition, Atlanta, October 29 2006-November 1 2006, pp. 2212- 2220.

[8] P. A. Tipler and A. Llewellyn, “Modern Physics,” 5th Edition, W. H. Freeman and Company, New York, 2007.

[9] J. M. Abe and J. I. Da Silva Filho, “Inconsistency and Electronic Circuits,” In: E. Alpaydin, Ed., Proceedings of EIS’98 International ICSC Symposium on Engineering of Intelligent Systems, Vol. 3, 1998, pp. 191-197.

[10] N. C. A. Da Costa, “On the Theory of Inconsistent Formal Systems,” Notre Dame Journal of Formal Logic, Vol. 15, No. 4, 1974, pp. 497-510. doi:10.1305/ndjfl/1093891487

[11] J. I. Da Silva Filho and A. Rocco, “Power Systems Outage Possibilities Analysis by Paraconsistent Logic,” 2008 IEEE Power and Energy Society General Meeting: Conversion and Delivery of Electrical Energy in the 21st Century, Pittsburgh, 20-24 July 2008, pp. 1-6.

[12] D. Kleppner and R. K. Binding: “An Introduction to Mechanics” Mcgraw-Hill, Columbus, 1973, p. 600.

[13] P. A. Tipler, “Physics,” Worth Publishers, Inc., New York, 1976.

[14] P. A Tipler and G. M. Tosca, “Physics for Scientists,” 6th Edition, W. H. Freeman and Company, 2007.

[15] J. Bernstein, P. M. Fishbane and S. G. Gasiorowicz “Modern Physics,” Prentice-Hall, New York, 2000, p. 624.

[16] J. P. Mckelvey and H. Grotch “Physics for Science and Engineering,” Harper and Row Publisher Inc., New York, 1978, p. 426.

[17] M. Ference Jr., H. B. Lemon and R. J. Stephenson “Analytical Experimental Physics,” 2nd Editon, University of Chicago Press, Chicago, 1956.

[18] J. A. Wheeler and H. Z. Wojciech (eds), “Quantum Theory and Measurement,” Princeton University Press, Princeton, 1983.

[19] H. A. Blair and V. S. Subrahmanian, “Paraconsistent Lo- gic Programming,” 7th Conference on Foundations of Software Technology and Theoretical Computer Science, Pune, 17-19 December 1987.

[20] N. C. A. da Costa, D. Krause and O. Bueno, “Paraconsistent Logics and Paraconsistency,” In: D. Jacquette, D. M. Gabbay, P. Thagard and J. Woods, Eds., Philosophy of Logic, Elsevier, Series Handbook of the Philosophy of Science, Vol. 5, 2006, pp. 655-781.

[21] H. Reichenbach, “Philosophic Foundations of Quantum Mechanics,” University of California Press, Berkeley, 1944.

[22] F. Gross, “Relativistic Quantum Mechanics and Field Theory,” John Wiley & Sons, Inc., Hoboken, 1993, p. 97.