Title | Expanding the propositional logic of a t-norm with truth-constants: completeness results for rational semantics |

Publication Type | Journal Article |

Year of Publication | 2010 |

Authors | Esteva F [1], Godo L [2], Noguera C [3] |

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

Volume | 14 |

Pagination | 273-284 |

Publisher | Springer |

Abstract | In this paper we consider the expansions of logics of a left-continuous t-norm with truth-constants from a subalgebra of the rational unit interval. From known results on standard semantics, we study completeness for these propositional logics with respect to chains de?ned over the rational unit interval with a special attention to the completeness with respect to the canonical chain, i.e. the algebra over $[0, 1] \cap Q$ where each truth-constant is interpreted in its corresponding rational truth-value. Finally, we study rational completeness results when we restrict ourselves to deductions between the so-called evaluated formulae. |