Paraconsistent Annotated Logic and Chaos Theory: Introducing the Fundamental Equations

Regarding the Physical Science and Engineering areas, there has been significant interest in finding new ways of applications of Chaos Theory in modeling dynamic systems. In this specific area of knowledge, Paraconsistent Logic (PL) in its expanded form, in which it uses annotations composed of two values (PAL2v), can offer a significant contribution. PAL2v has been applied at the interpretation and modeling of physical systems showing very promising results. In this initial research, we are making analogies between the main foundations of PAL2v and the equation of Logistic Map of Verhulst who originated the modern Chaos Theory and its variations. The results of this comparison show that the procedures used in the application of the Logistic Map identify the Chaos Theory with paraconsistent analysis based on the fundamental concepts of PAL2v. Moreover, based on joint interpretations of PAL2v and Chaos Theory, fundamental equations are created called “ParaCaos equations”. With the equations obtained by the method of PAL2v analysis in Chaos Theory, there arises significant ways of research about the behavior and stability of chaotic systems. It is observed that the values that identify the PL state of the attractor of stability located on the PAL2v Lattice have a strong relationship with the golden ratio of geometry. Therefore, the equations extracted from the junction PAL2v and Chaos Theory can be used to identify the parameters of stability levels in complex systems and other applications.