Title | **On logical fiberings and automated deduction in many-valued logics using Gr\"obner bases.** |

Author(s) | Jochen Pfalzgraf |

Type | Article in Journal |

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. |

ISSN | 1578-7303 |

URL |
https://eudml.org/doc/41048 |

Language | English |

Journal | RACSAM, Rev. R. Acad. Cienc. Exactas F |

Volume | 98 |

Number | 1-2 |

Pages | 213--227 |

Publisher | Real Academia de Ciencias, Madrid |

Year | 2004 |

Edition | 0 |

Translation |
No |

Refereed |
No |