Título | On the set of intermediate logics between the truth and degree preserving Lukasiewicz logics |

Publication Type | Journal Article |

Year of Publication | 2016 |

Authors | Coniglio M [1], Esteva F [2], Godo L [3] |

Journal | Logic Journal of the IGPL |

Volume | 24 |

Incidencia | 3 |

Paginación | 288-320 |

Resumen | The aim of this paper is to explore the class of intermediate logics between the truth-preserving Lukasiewicz logic Łand its degree-preserving companion \L^{\leq}. From a syntactical point of view, we introduce some families of inference rules (that generalize the explosion rule) that are admissible in \L^{\leq} and derivable in Łand we characterize the corresponding intermediate logics. From a semantical point of view, we first consider the family of logics characterized by matrices defined by lattice filters in [0, 1], but we show there are intermediate logics falling outside this family. Finally,we study the case of finite-valued Lukasiewicz logics where we axiomatize a large family of intermediate logics defined by families of matrices (A,F) such that A is a finite MV-algebra and F is a lattice filter. |