Journal of Philosophical Logic (2-3):1-30 (2013)

María Manzano
Universidad de Salamanca
Patrick Blackburn
Roskilde University
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 [email protected]_i$ in propositional and first-order hybrid logic. This means: interpret [email protected]_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 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
Keywords Hybrid logic  Type theory  Higher-order modal logic  Nominals  @ operators
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DOI 10.1007/s10992-012-9260-4
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References found in this work BETA

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Citations of this work BETA

Completeness: From Gödel to Henkin.Maria Manzano & Enrique Alonso - 2014 - History and Philosophy of Logic 35 (1):1-26.
The Logic of Imaginary Scenarios.Joan Casas-Roma, Antonia Huertas & M. Elena Rodríguez - 2020 - Logic Journal of the IGPL 28 (3):363-388.

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