Calculus for a multivalued-logic algebraic system

摘要

The direct and inverse derivatives, differential, differential expression, compatible and exact integrals, etc., known for Booleab algebraic systems (where m, the number of levels, is 2) are generalized for a multivalued-logic (MVL) algebra where m ⩾ 3. Ways of finding the derivatives are given, differential matrices and differential- expression matrices are defined, and a necessary and sufficient condition for compatible integrability of a given differential-expression matrix is given. Also, a method for finding distinct compatible integrals for an integrable differential expression matrix is given. Just like their Boolean counterparts, the MVL derivatives have applications in the analysis of faults in a multivated logic network, and the integration of MVL differential expression matrices has applications in the synthesis of MVL networks.