Paraconsistent Annotated Logic in Analysis of Physical Systems: Introducing the Paraquantum Factor of Quantization hψ

Author(s)
João Inácio Da Silva Filho

ABSTRACT

We present in this paper an alternative of modeling physical systems through a non-Classical logic namely the Paraconsistent Logic (PL) whose main feature is the revocation of the principle of non-contradiction. The Paraconsistent Annotated Logic with annotation of two values (PAL2v) is a type of PL and has in its theoretical structure the main feature of dealing with contradictions offering flexibility in drawing conclusions. Several works about applications of PAL2v have shown that such logic is able to provide us with an adequate treatment to uncertainties. Based on the foundations of the PAL2v we presented the ParaQuantum logic (PQL) with the goal of performing analysis of signals from information sources which model physical systems. The formalization of the concepts of the logics PQL, that it is represented in a Lattice, requires the considering of Paraquantum logical states ψ which are propagated through variations of the evidence Degrees µ and λ which come out from measurements performed in Observable Variables in the physical world. When we analyze the lattice of the PQL, we obtain equations which quantify values of physical quantities from where we obtain the effects of propagation of the Paraquantum logical states ψ. In this paper, we introduce the Paraquantum Factor of quantization hψ whose value is associated with a special logical state on the lattice which is identified with the Planck constant h. We conclude through these studies that the Paraquantum Logical Model based on the ParaQuantum logics PQL can link the several fields of the physical sciences by means of quantization of values. It is an innovative approach of formulating natural phenomena.

We present in this paper an alternative of modeling physical systems through a non-Classical logic namely the Paraconsistent Logic (PL) whose main feature is the revocation of the principle of non-contradiction. The Paraconsistent Annotated Logic with annotation of two values (PAL2v) is a type of PL and has in its theoretical structure the main feature of dealing with contradictions offering flexibility in drawing conclusions. Several works about applications of PAL2v have shown that such logic is able to provide us with an adequate treatment to uncertainties. Based on the foundations of the PAL2v we presented the ParaQuantum logic (PQL) with the goal of performing analysis of signals from information sources which model physical systems. The formalization of the concepts of the logics PQL, that it is represented in a Lattice, requires the considering of Paraquantum logical states ψ which are propagated through variations of the evidence Degrees µ and λ which come out from measurements performed in Observable Variables in the physical world. When we analyze the lattice of the PQL, we obtain equations which quantify values of physical quantities from where we obtain the effects of propagation of the Paraquantum logical states ψ. In this paper, we introduce the Paraquantum Factor of quantization hψ whose value is associated with a special logical state on the lattice which is identified with the Planck constant h. We conclude through these studies that the Paraquantum Logical Model based on the ParaQuantum logics PQL can link the several fields of the physical sciences by means of quantization of values. It is an innovative approach of formulating natural phenomena.

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, "Paraconsistent Annotated Logic in Analysis of Physical Systems: Introducing the Paraquantum Factor of Quantization hψ,"*Journal of Modern Physics*, Vol. 2 No. 11, 2011, pp. 1397-1409. doi: 10.4236/jmp.2011.211172.

nullJ. Filho, "Paraconsistent Annotated Logic in Analysis of Physical Systems: Introducing the Paraquantum Factor of Quantization hψ,"

References

[1] S. Jas’kowski, “Propositional Calculus for Contradictory Deductive Systems,” Studia Logica, Vol. 24, 1969, pp. 143-157. doi:10.1007/BF02134311

[2] 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

[3] N. C. A. Da Costa and D. Marconi, “An Overview of Paraconsistent Logic in the 80’s,” The Journal of Non- Classical Logic, Vol. 6, 1989, pp. 5-31.

[4] N. C. A. Da Costa, V. S. Subrahmanian and C. Vago, “The Paraconsistent Logic PT,” Zeitschrift fur Mathematische Logik und Grundlagen der Mathematik, Vol. 37, 1991, pp. 139-148. doi:10.1002/malq.19910370903

[5] R. Anand and V. S. Subrahmanian, “A Logic Programming System Based on a Six-Valued Logic,” AAAI/Xerox Second International Symposium on Knowledge Engineering, Madrid, 1987.

[6] V. S. Subrahmanian, “On the Semantics of Quantitative Lógic Programs,” Proceedings of 4th IEEE Symposium on Logic Programming, Computer Society Press, Washington D.C, 1987.

[7] D. Krause and O. Bueno, “Scientific Theories, Models, and the Semantic Approach,” Principia, Vol. 11, No. 2, 2007, pp. 187-201.

[8] J. I. Da Silva Filho, G. Lambert-Torres and J. M. Abe, “Uncertainty Treatment Using Paraconsistent Logic - Introducing Paraconsistent Artificial Neural Networks,” Vol. 211, IOS Press, Amsterdam, 2010, p. 328.

[9] 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,” IEEE Power Engineering Society—PSC 2006 Power System Conference and Exposition, Atlanta, 29 October-1 November 2006, pp. 2212-2220.

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

[11] C. A. Fuchs and A. Peres, “Quantum Theory Needs no ‘Interpretation’,” Physics Today, Vol. 53, No. 3, March 2000, pp. 70-71.

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

[13] M. Jammer, “The Philosophy of Quantum Mechanics,” Wiley, New York, 1974.

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

[15] Pl. A. Tipler, “Physics,” Worth Publishers Inc, New York, 1976

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

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

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

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

[1] S. Jas’kowski, “Propositional Calculus for Contradictory Deductive Systems,” Studia Logica, Vol. 24, 1969, pp. 143-157. doi:10.1007/BF02134311

[2] 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

[3] N. C. A. Da Costa and D. Marconi, “An Overview of Paraconsistent Logic in the 80’s,” The Journal of Non- Classical Logic, Vol. 6, 1989, pp. 5-31.

[4] N. C. A. Da Costa, V. S. Subrahmanian and C. Vago, “The Paraconsistent Logic PT,” Zeitschrift fur Mathematische Logik und Grundlagen der Mathematik, Vol. 37, 1991, pp. 139-148. doi:10.1002/malq.19910370903

[5] R. Anand and V. S. Subrahmanian, “A Logic Programming System Based on a Six-Valued Logic,” AAAI/Xerox Second International Symposium on Knowledge Engineering, Madrid, 1987.

[6] V. S. Subrahmanian, “On the Semantics of Quantitative Lógic Programs,” Proceedings of 4th IEEE Symposium on Logic Programming, Computer Society Press, Washington D.C, 1987.

[7] D. Krause and O. Bueno, “Scientific Theories, Models, and the Semantic Approach,” Principia, Vol. 11, No. 2, 2007, pp. 187-201.

[8] J. I. Da Silva Filho, G. Lambert-Torres and J. M. Abe, “Uncertainty Treatment Using Paraconsistent Logic - Introducing Paraconsistent Artificial Neural Networks,” Vol. 211, IOS Press, Amsterdam, 2010, p. 328.

[9] 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,” IEEE Power Engineering Society—PSC 2006 Power System Conference and Exposition, Atlanta, 29 October-1 November 2006, pp. 2212-2220.

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

[11] C. A. Fuchs and A. Peres, “Quantum Theory Needs no ‘Interpretation’,” Physics Today, Vol. 53, No. 3, March 2000, pp. 70-71.

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

[13] M. Jammer, “The Philosophy of Quantum Mechanics,” Wiley, New York, 1974.

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

[15] Pl. A. Tipler, “Physics,” Worth Publishers Inc, New York, 1976

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

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

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

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