# Completeness in Hybrid Type Theory

Title | Completeness in Hybrid Type Theory |

Publication Type | Journal Article |

Year of Publication | 2014 |

Authors | Areces, C, Blackburn, P, Huertas, A.,, Manzano, M |

Journal | Journal of Philosophical Logic |

Volume | 43 |

Pagination | 209–238 |

Date Published | June |

Abstract | We show that basic hybridization (adding nominals and @ operators) makes it possible to give straightforward Henkin-style completeness proofs even when the modal logic being hybridized is higher-order. The key ideas are to add nominals as expressions of type t, and to extend to arbitrary types the way we interpret @i in propositional and first-order hybrid logic. This means: interpret @i \alpha_a, where \alpha_a is an expression of any type a, as an expression of type a that rigidly returns the value that \alpha_a receives at the i-world. The axiomatization and completeness proofs are generalizations of those found in propositional and first-order hybrid logic, and (as is usual in hybrid logic) we automatically obtain a wide range of completeness results for stronger logics and languages. Our approach is deliberately low-tech. We don't, for example, make use of Montague's intensional type s, or Fitting-style intensional models; we build, as simply as we can, hybrid logic over Henkin's logic. |

Work Package:

WP2