TITLE:
An Introduction to Paraconsistent Integral Differential Calculus: With Application Examples
AUTHORS:
João Inácio Da Silva Filho
KEYWORDS:
Paraconsistent Logic, Paraconsistent Annotated Logic, Paraconsistent Mathematics, Paraconsistent Integral Differential Calculus
JOURNAL NAME:
Applied Mathematics,
Vol.5 No.6,
April
8,
2014
ABSTRACT: 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.