Título | On the Hierarchy of t-norm Based Residuated Fuzzy Logics |

Publication Type | Book Chapter |

Year of Publication | 2003 |

Authors | Esteva F [1], Godo L [2], García-Cerdaña A [3] |

Editor | [4] |

Book Title | Beyond Two: Theory and Applications of Multiple-Valued Logic |

Paginación | 251-272 |

Editorial | Physica-Verlag |

Resumen | In this paper we overview recent results, both logical and algebraic, about [0,1]-valued logical systems having a t-norm and its residuum as truth functions for conjunction and implication. We describe their axiomatic systems and algebraic varieties and show they can be suitably placed in a hierarchy of logics depending on their characteristic axioms. We stress that the most general variety generated by residuated structures in [0,1], which are defined by left-continuous t-norms, is not the variety of residuated lattices but the variety of pre-linear residuated lattices, also known as MTL-algebras. Finally, we also relate t-norm based logics to substructural logics to substructural logics, in particular to Ono's hierarchy of extensions of the Full Lambek Calculus. |