Why Some Non-classical Logics Are More Studied?

  • Olga Kosheleva
  • Vladik KreinovichEmail author
  • Hoang Phuong Nguyen
Part of the Studies in Computational Intelligence book series (SCI, volume 899)


It is well known that the traditional 2-valued logic is only an approximation to how we actually reason. To provide a more adequate description of how we actually reason, researchers proposed and studied many generalizations and modifications of the traditional logic, generalizations and modifications in which some rules of the traditional logic are no longer valid. Interestingly, for some of such rules (e.g., for law of excluded middle), we have a century of research in logics that violate this rule, while for others (e.g., commutativity of “and”), practically no research has been done. In this paper, we show that fuzzy ideas can help explain why some non-classical logics are more studied and some less studied: namely, it turns out that most studied are the violations which can be implemented by the simplest expressions (specifically, by polynomials of the lowest order).



This work was supported in part by the National Science Foundation via grants 1623190 (A Model of Change for Preparing a New Generation for Professional Practice in Computer Science) and HRD-1242122 (Cyber-ShARE Center of Excellence).


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Copyright information

© The Editor(s) (if applicable) and The Author(s), under exclusive license to Springer Nature Switzerland AG 2021

Authors and Affiliations

  • Olga Kosheleva
    • 1
  • Vladik Kreinovich
    • 1
    Email author
  • Hoang Phuong Nguyen
    • 2
  1. 1.University of Texas at El PasoEl PasoUSA
  2. 2.Division Informatics, Math-Informatics FacultyThang Long UniversityHanoiVietnam

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