Paraconsistent Annotated Logic in Analysis of Physical Systems:Introducing the Paraquantum Factor of Quantization h_(ψ)

We present in this paper an alternative of modeling physical systems through a non-Classical logic namely the Paraconsistent Logic (PL) whose main feature is the revocation of the principle of non-contradiction. The Paraconsistent Annotated Logic with annotation of two values (PAL2v) is a type of PL and has in its theoretical structure the main feature of dealing with contradictions offering flexibility in drawing conclusions. Several works about applications of PAL2v have shown that such logic is able to provide us with an adequate treatment to uncertainties. Based on the foundations of the PAL2v we presented the ParaQuantum logic (PQL) with the goal of performing analysis of signals from information sources which model physical systems. The formalization of the concepts of the logics PQL, that it is represented in a Lattice, requires the considering of Paraquantum logical states ψ which are propagated through variations of the evidence Degrees μ and λ which come out from measurements performed in Observable Variables in the physical world. When we analyze the lattice of the PQL, we obtain equations which quantify values of physical quantities from where we obtain the effects of propagation of the Paraquantum logical states ψ. In this paper, we introduce the Paraquantum Factor of quantization hψ whose value is associated with a special logical state on the lattice which is identified with the Planck constant h. We conclude through these studies that the Paraquantum Logical Model based on the ParaQuantum logics PQL can link the several fields of the physical sciences by means of quantization of values. It is an innovative approach of formulating natural phenomena.

An Application of Paraconsistent Annotated Logic for Design Software Testing Strategies

Nowadays, application model systems for decision-making based on non-classical logic such as Paraconsistent Logic are used successfully in the treatment of uncertainties. The method presented in this paper is based on the fundamental concepts of Paraconsistent Annotated Logic with annotation of 2 values (PAL2v). In this study, two algorithms based on PAL2v are presented gradually, to extract the effects of the contradiction in signals of information from a database of uncertain knowledge. The Paraconsistent Extractors Algorithms of Contradiction Effect-Para Extrctr is applied to filters of networks of analyses (PANets) of signal information, where uncertain and contradictory signals may be found. Software test case scenarios are subordinated to an application model of Paraconsistent decision-making, which provides an analysis using Paraconsistent Logic in the treatment of uncertainties for design software testing strategies. This quality-quantity criterion to evaluate the software product quality is based on the characteristics of software testability analysis. The Para consistent reasoning application model system presented in this case study, reveals itself to be more efficient than the traditional methods because it has the potential to offer an appropriate treatment to different originally contradicting source information.

Treatment of Uncertainties with Algorithms of the Paraconsistent Annotated Logic

The method presented in this work is based on the fundamental concepts of Paraconsistent Annotated Logic with annotation of 2 values (PAL2v). The PAL2v is a non-classic Logics which admits contradiction and in this paper we perform a study using mathematical interpretation in its representative lattice. This studies result in algorithms and equations give an effective treatment on signals of information that represent situations found in uncertainty knowledge database. From the obtained equations, algorithms are elaborated to be utilized in computation models of the uncertainty treatment Systems. We presented some results that were obtained of analyses done with one of the algorithms that compose the paraconsistent analyzing system of logical signals with the PAL2v Logic. The paraconsistent reasoning system built according to the PAL2v methodology notions reveals itself to be more efficient than the traditional ones, because it gets to offer an appropriate treatment to contradictory information.

Introducing the Paraquantum Equations and Applications

In this paper, we present an equationing method based on non-classical logics applied to resolution of problems which involves phenomena of physical science. A non-classical logic denominated of the Paraquantum Logic (PQL), which is based on the fundamental concepts of the Paraconsistent Annotated logic with annotation of two values (PAL2v), is used. The formalizations of the PQL concepts, which are represented by a lattice with four vertices, lead us to consider Paraquantum logical states ψ which are propagated by means of variations of the evidence Degrees extracted from measurements performed on the Observable Variables of the physical world. The studies on the lattice of PQL give us equations that quantify values of physical largenesses from where we obtain the effects of the propagation of the Paraquantum logical states ψ. The PQL lattice with such features can be extensively studied and we obtain a Paraquantum Logical Model with the capacity of contraction or expansion which can represent any physical universe. In this paper the Paraquantum Logical Model is applied to the Newton Laws where we obtain equations and verify the action of an expansion factor the PQL lattice called Paraquantum Gamma Factor γPψ and its correlation with another important factor called Paraquantum Factor of quantization hψ. We present numerical examples applied to real physical systems through the equations which deal with paraquantum physical largenesses and how these values are transmitted to the physical world. With the results of these studies we can verify that the Paraquantum Logical Model has the property of interconnect several fields of the Physical Science.

An Introduction to Paraconsistent Integral Differential Calculus:With Application Examples

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.