Ebook: Uncertainty Treatment Using Paraconsistent Logic
In the past, control systems for automation and robotics and the expert systems employed in artificial intelligence were generally based on classical, or Boolean, logic. However, this proved to be inadequate by virtue of its binary nature, for portraying the uncertainties and inconsistencies of the ‘real’ world, and so from the late 1990s, research has been ongoing into the application of paraconsistent, or non-classical logics in these fields. This book aggregates much of this research, from 1999 up to the present. Organized to facilitate an understanding of the theory and the development of the applied methods, "Uncertainty Treatment Using Praconsistent Logic" presents the material in a sequential fashion and is divided into three parts. Notions of Paraconsistent Annotated Logic (PAL) summarizes the basic theory and fundamentals of the subject. The second part, Paraconsistent Analysis Networks (PANets), describes the utilization of paraconsistent logic in constructing networks which can deal with representative data from uncertain information. The final section, Paraconsistent Artificial Neural Networks (PANNets), is composed of six chapters which chart the applications of PAL, from a comparison between Paraconsistent Analysis Nodes (PANs) and the action of the human brain through to complex PANNet architecture capable of processing signals inspired by human brain function. This invaluable state-of-the-art overview will be of interest to all those involved with the development of robotics or artificial intelligence and will serve as reference for future application of paraconsistent logics in all computer and electronic systems.
Several strictly theoretical papers present Paraconsistent Logic as a good solution to carry out treatment of situations where the Classical Logic is ineffectual or unable to be applied, due to being binary. These situations like the ambiguities, lack of definition (indefinition), and mainly the inconsistencies often appear and are frequently described in the real.
By the end of last century, some interesting work that showed the applications of Paraconsistent Logic in several areas of Artificial Intelligence had already appeared in Brazil, mainly at the Polytechnic School of the University of São Paulo. In the 1990s, among the countless papers presented, the “Methods of Applications of Paraconsistent Annotated Logic with annotation of two values (PAL2v) with Construction of Algorithm and Implementation of Electronic Circuits” stood out. It was defended in 1999 by one of the authors of this book, and from then on, has become a reference material for various researches on the applications of Paraconsistent Logic. Defended in 1999, the thesis brought Paraconsistent Logic from a strictly theoretical field into a simpler, practical, and direct application, enabling Control Systems to carry out treatment of situations uncovered by Classical Logic and thus conquering a significant advance in the way of treating contradictory signals. The methods were based on a class of Non-Classical Logic, which was named Paraconsistent Annotated Logic with annotation of two values (PAL2v).
The signal analysis utilizing PAL2v permitted several problems caused by contradictory and paracomplete situations to be treated in a way closer to reality, through consideration of evidences. This interpretation method has brought relevant results that led to the construction of the algorithm named “Para-Analyzer”, which implemented in conventional computer language, provides direct application of the concepts of Paraconsistent Logic in Control Systems, Automation and Robotics. Still in this work presented in 1999, various suggestions were also offered on the application of a Paraconsistent Logic Controller (Para-Control) in Control Systems. The Para-Control, demonstrated, for the first time, the applicability of Paraconsistent Logics in real and functional Systems and the concepts and methods presented there produced several Master and PhD thesis related to the application of PAL2v in other fields of knowledge.
From this initial work, new researches have been done on the applications, and the basic concepts of PAL2v are presented in this book with a few changes, bringing remodeled and adapted nomenclature, aggregating the new contributions, which appeared from 1999 until now. With these adaptations and new considerations, like the calculus of the Real Degree of Certainty, and the Interval of Certainty, the reach of the PAL2v applications becomes wider and introduces precision and greater robustness in the Systems applying PAL2v for analysis and decision.
The formation of Paraconsistent Analysis Systems, or Paraconsistent Analysis Nodes (PANs) as named in this work, acting in Paraconsistent Analysis Networks for decision making and Paraconsistent Artificial Neural Cells (PANCs) interconnected into Paraconsistent Artificial Neural Networks, promote an Uncertainty Treatment forcing the System to give an answer. This innovating form of Uncertainty Treatment enables the method presented in this book to be utilized in Systems, which deals with data originated from Uncertain Knowledge information banks, without the weight of conflict invalidating the calculus for decision making.
A few examples of projects and Systems that utilize the methods with their main algorithms accompany this book. Despite being directed to determined areas, these examples motivate the implementation of new and promising Uncertainty Treatment Systems with Paraconsistent Logic in several other fields of knowledge.
The authors would like to thank Professor Luis Fernando Pompeu Ferrara and Professor Maurício C. Mário for the support in the test with the Learning Paraconsistent Artificial Neural Cell (lPANC) and the Computer Engineering student at UNISANTA – Santa Cecília University-Santos-ESP, Brazil – Gilberto T. A. Holms for the help in the validation of the PAL2v algorithms.
Also the authors would like to express their gratitude to Prof. Helga Gonzaga Martins and Zilma de Castro for the work of translation of this book.