TITLE:
Paraconsistent Differential Calculus (Part I): First-Order Paraconsistent Derivative
AUTHORS:
João Inácio Da Silva Filho
KEYWORDS:
Paraconsistent Logic, Paraconsistent Annotated Logic, Paraconsistent Mathematics, Paraconsistent Differential Calculus
JOURNAL NAME:
Applied Mathematics,
Vol.5 No.6,
April
8,
2014
ABSTRACT: A type of Inconsistent Mathematics structured on Paraconsistent Logic
(PL) and that has, as the main purpose, the study of common mathematical
objects such as sets, numbers and functions, where some contradictions are
allowed, is called Paraconsistent Mathematics. The PL is a non-Classical logic
and its main property is to present tolerance for contradiction in its
fundamentals without the invalidation of the conclusions. In this paper (part
1), we use the PL in its annotated form, denominated Paraconsistent Annotated
Logic with annotation of two values—PAL2v for present a first-order Paraconsistent
Derivative. The PAL2v has, in its representation, an associated lattice FOUR
based on Hasse Diagram. This PAL2v-Lattice
allows development of a Para-consistent Differential Calculus based on
fundamentals and equations obtained by geometric interpretations. In this first
article it is presented some examples applying derivatives of first-order with
the concepts of Paraconsistent Mathematics. In the second part of this work we
will show the Paraconsistent Derivative of second-order with application
examples.