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• W2029151503 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 $@_ialpha _a$ , 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 inhybrid 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 logicover Henkin’s logic." @default.
• W2029151503 created "2016-06-24" @default.
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• W2029151503 date "2013-01-10" @default.
• W2029151503 modified "2023-10-01" @default.
• W2029151503 title "Completeness in Hybrid Type Theory" @default.
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• W2029151503 doi "https://doi.org/10.1007/s10992-012-9260-4" @default.
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