Title | On strong standard completeness in some MTL$_\Delta$ expansions |

Publication Type | Journal Article |

Year of Publication | 2017 |

Authors | Vidal A, Bou F, Esteva F, Godo L |

Journal | Soft Computing - A Fusion of Foundations, Methodologies and Applications |

Volume | 21 |

Issue | 1 |

Pagination | 125-147 |

Abstract | In this paper, inspired by the previous work of Franco Montagna on infinitary axiomatizations for standard BL-algebras, we focus on a uniform approach to the following problem: given a left-continuous t-norm *, find an axiomatic system (possibly with infinitary rules) which is strongly complete with respect to the standard algebra $[0, 1]_*$. This system will be an expansion of MTL (Monoidal t-norm based logic). First, we introduce an infinitary axiomatic system $L^\infty_*$, expanding the language with Delta and countably many truth-constants, and with only one infinitary inference rule, that is inspired in Takeuti-Titani density rule. Then we show that $L^\infty_*$ is indeed strongly complete with respect to the standard algebra $[0,1]_*$. Moreover, the approach is generalized to axiomatize expansions of these logics with additional operators whose intended semantics over [0,1] satisfy some regularity conditions. |

URL | http://link.springer.com/article/10.1007%2Fs00500-016-2338-0 |