Prime implicant-implicate generating algorithms for multiple-valued logics (MVL's) are introduced. Techniques from classical logic not requiring large normal forms or truth tables are adapted to certain regular'' multiple-valued logics. This is accomplished by means of signed formulas, a meta-logic for multiple valued logics; the formulas are normalized in a way analogous to negation normal form. The logic of signed formulas is classical in nature. The presented method is based on path dissolution, a strongly complete inference rule. The generalization of dissolution that accommodates signed formulas is described. The method is first characterized as a procedure iterated over the truth value domain ∆ = {0,1, ... ,n-1} of the MVL. The computational requirements are then reduced via parameterization with respect to the elements and the cardinality of ∆.
@article{urn:eudml:doc:39102,
title = {Parametrized prime implicant-implicate computations for regular logics.},
journal = {Mathware and Soft Computing},
volume = {4},
year = {1997},
pages = {155-179},
zbl = {0880.03010},
mrnumber = {MR1621914},
language = {en},
url = {http://dml.mathdoc.fr/item/urn:eudml:doc:39102}
}
Ramesh, Anavai; Murray, Neil V. Parametrized prime implicant-implicate computations for regular logics.. Mathware and Soft Computing, Tome 4 (1997) pp. 155-179. http://gdmltest.u-ga.fr/item/urn:eudml:doc:39102/