# On logical fiberings and automated deduction in many-valued logics using Gröbner bases.

RACSAM (2004)

- Volume: 98, Issue: 1, page 213-227
- ISSN: 1578-7303

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topPfalzgraf, Jochen. "On logical fiberings and automated deduction in many-valued logics using Gröbner bases.." RACSAM 98.1 (2004): 213-227. <http://eudml.org/doc/41048>.

@article{Pfalzgraf2004,

abstract = {The concept of logical fiberings is briefly summarized. Based on experiences with concrete examples an algorithmic approach is developed which leads to a represention of a many-valued logic as a logical fibering. The Stone isomorphism for expressing classical logical operations by corresponding polynomials can be extended to m-valued logics. On the basis of this, a classical deduction problem can be treated symbolically as a corresponding ideal membership problem using computer algebra support with the method of Gröbner bases. A logical fibering representation in this context provides a parallelization of the original problem and leads to (fiberwise) simpler polynomials and thus to a reduction of complexity.},

author = {Pfalzgraf, Jochen},

journal = {RACSAM},

keywords = {logical fibering; Gröbner basis; many-valued logic},

language = {eng},

number = {1},

pages = {213-227},

title = {On logical fiberings and automated deduction in many-valued logics using Gröbner bases.},

url = {http://eudml.org/doc/41048},

volume = {98},

year = {2004},

}

TY - JOUR

AU - Pfalzgraf, Jochen

TI - On logical fiberings and automated deduction in many-valued logics using Gröbner bases.

JO - RACSAM

PY - 2004

VL - 98

IS - 1

SP - 213

EP - 227

AB - The concept of logical fiberings is briefly summarized. Based on experiences with concrete examples an algorithmic approach is developed which leads to a represention of a many-valued logic as a logical fibering. The Stone isomorphism for expressing classical logical operations by corresponding polynomials can be extended to m-valued logics. On the basis of this, a classical deduction problem can be treated symbolically as a corresponding ideal membership problem using computer algebra support with the method of Gröbner bases. A logical fibering representation in this context provides a parallelization of the original problem and leads to (fiberwise) simpler polynomials and thus to a reduction of complexity.

LA - eng

KW - logical fibering; Gröbner basis; many-valued logic

UR - http://eudml.org/doc/41048

ER -

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