# Parametrized prime implicant-implicate computations for regular logics. Parametrized prime implicant/implicate computations for regular logics.

• Volume: 4, Issue: 2, page 155-179
• ISSN: 1134-5632

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## Abstract

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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 ∆.

## How to cite

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Ramesh, Anavai, and Murray, Neil V.. "Parametrized prime implicant-implicate computations for regular logics.." Mathware and Soft Computing 4.2 (1997): 155-179. <http://eudml.org/doc/39102>.

@article{Ramesh1997,
abstract = {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 ∆.},
author = {Ramesh, Anavai, Murray, Neil V.},
journal = {Mathware and Soft Computing},
keywords = {Lógica multivaluada; Algoritmos; Signatura; Formulación; Parametrización; many-valued logic; Post logic; prime implicants; prime implicates; algorithms; negation normal form; logic of signed formulas; path dissolution},
language = {eng},
number = {2},
pages = {155-179},
title = {Parametrized prime implicant-implicate computations for regular logics.},
url = {http://eudml.org/doc/39102},
volume = {4},
year = {1997},
}

TY - JOUR
AU - Ramesh, Anavai
AU - Murray, Neil V.
TI - Parametrized prime implicant-implicate computations for regular logics.
JO - Mathware and Soft Computing
PY - 1997
VL - 4
IS - 2
SP - 155
EP - 179
AB - 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 ∆.
LA - eng
KW - Lógica multivaluada; Algoritmos; Signatura; Formulación; Parametrización; many-valued logic; Post logic; prime implicants; prime implicates; algorithms; negation normal form; logic of signed formulas; path dissolution
UR - http://eudml.org/doc/39102
ER -

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