http://www.scirp.org/journal/PaperInformation.aspx?PaperID=44593
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João Inácio Da Silva Filho
In this paper we show that it is possible to
integrate functions with concepts and fundamentals of Paraconsistent Logic (PL).
The PL is a non-classical Logic that tolerates the contradiction without
trivializing its results. In several works the PL in his annotated form, called
Paraconsistent logic annotated with annotation of two values (PAL2v), has
presented good results in analysis of information signals. Geometric
interpretations based on PAL2v-Lattice associate were obtained forms of
Differential Calculus to a Paraconsistent Derivative of first and second-order
functions. Now, in this paper we extend the calculations for a form of
Paraconsistent Integral Calculus that can be viewed through the analysis in the
PAL2v-Lattice. Despite improvements that can develop calculations in complex
functions, it is verified that the use of Paraconsistent Mathematics in
differential and Integral Calculus opens a promising path in researches
developed for solving linear and nonlinear systems. Therefore the Paraconsistent
Integral Differential Calculus can be an important tool in systems by modeling
and solving problems related to Physical Sciences.
KEYWORDS
Paraconsistent Logic, Paraconsistent Annotated Logic, Paraconsistent Mathematics, Paraconsistent Integral Differential Calculus
Cite this paper
Da Silva Filho, J. I. (2014) An Introduction to
Paraconsistent Integral Differential Calculus: With Application Examples.
Applied Mathematics, 5, 949-962. doi: 10.4236/am.2014.56090.