Abstract
This paper is a continuation of the first part in which characterization of simple logics without tautologies (LWT) are provided. In this part, LWT determined by finite matrices with a more complex algebraic structure, possessing from 2 to 6 functions, are examined. Diagrams showing the lattice structure of the studied families of logics are presented. The total number of investigated systems is greater than 90. At the end the diagram showing mutual relations holding between the investigated LWTs is presented.
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