Revistes Catalanes amb Accés Obert (RACO)

Parameterized prime implicant/implicate computations for regular logics

Anavi Ramesh, Neil V. Murray


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 $\Delta\,=\,\{0,1, \dots ,n-1\}$ of the MVL. The computational requirements are then reduced via parameterization with respect to the elements and the cardinality of $\Delta$.

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