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

Jochen Pfalzgraf

RACSAM (2004)

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

Abstract

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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.

How to cite

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Pfalzgraf, 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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