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Nonclassical logics and multivariate truth values

Volodymyr M. Zhuravlov

Abstract

The article demonstrates that logic is not necessarily singleton and does not always have the standard interpretation of negation. Appropriate generalizations of logic are suggested. Positive logic and multivalued negation operations are examined. An attempt is made to abstract from the fixed and absolute values of truth and falsehood; the ambiguity of logical values is interpreted as their relativity, projective logic.

Nonclassical logics and multivariate truth values

Abstract

The article demonstrates that logic is not necessarily singleton and does not always have the standard interpretation of negation. Appropriate generalizations of logic are suggested. Positive logic and multivalued negation operations are examined. An attempt is made to abstract from the fixed and absolute values of truth and falsehood; the ambiguity of logical values is interpreted as their relativity, projective logic.
Paper Structure (7 sections, 15 equations)

This paper contains 7 sections, 15 equations.

Table of Contents

  1. Introduction
  2. Cyclic many-valued logics with varying truth
  3. Vector logic
  4. Non-singleton logic
  5. Projective logic
  6. A note on the semantics of Galois correspondences
  7. References