Calculus for a multivalued-logic algebraic system
MOIEZ A. TAPIA, TAYEB A. GUIMA, ABDOLLAH KATBAB · Applied Mathematics and Computation · 1991
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.