Maple Information Tools in the Study of Mathematical Logic Questions

Abstract

Correspondence (truth) tables are the main model for the analysis of various logical expressions. Their applications go beyond the study of Boolean algebra. The Maple computer algebra system has a wide range of commands for working with propositions, obtaining and evaluating their truth, but the result of their execution is most often not represented in a perfectly normal form. The results obtained are undoubtedly useful, but do not contribute to the development of competencies in the field of modeling Boolean functions. In this case, using the programming methods of the Maple computer algebra system, as well as its ability to create interactive applications. The article presents the results of a study summarizing the experience of implementing computer algebra systems for modeling logical functions. To expand the possibilities, comply with the requirements of interactivity, the Maple computer algebra system was chosen as the main tool. The developed and presented interactive application allows you to automatically build Boolean functions based on their truth or falsity values and present the result in the form of perfect disjunctive or conjunctive normal forms. The authors presented the features of using the developed application. The main goal: to achieve an understanding of the process of building a model of Boolean functions, presented in a perfect disjunctive or conjunctive form, to help in the study of discrete mathematics, students of both technical and humanitarian specialties. In addition, evaluate your knowledge in this discipline.

Information modeling of the normal forms of logical functions in Maple system

“…It is well known that the Maple computer algebra system (CAS) is a mathematical system that operates and processes information in symbolic or algebraic form [4,5]. Using Maple, it is possible to obtain an accurate analytical solution to mathematical problems [6], including integrals, systems of equations, differential equations, linear algebra problems [7], cryptography [8][9][10], discrete mathematics, including mathematical logic [11][12][13]. Maple also contains a large set of built-in functions, graphical procedures for evaluating and solving mathematical problems where exact solutions do not exist.…”

Information and logical transformations in Schaeffer and Pierce Bases in Maple

“…We present an algorithm for the transition from the minimal disjunctive normal form (DNF) to the Schaeffer basis. Consider a function for n variables [31][32][33]:…”