Journal of Philosophical Logic 43 (2-3):209-238 (2014)

María Manzano
Universidad de Salamanca
Patrick Blackburn
Roskilde University
We show that basic hybridization 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 \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$@_i$\end{document} in propositional and first-order hybrid logic. This means: interpret \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$@_i\alpha _a$\end{document}, where \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$\alpha _a$\end{document} is an expression of any type \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$a$\end{document}, as an expression of type \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$a$\end{document} that rigidly returns the value that \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$\alpha_a$\end{document} receives at the i-world. The axiomatization and completeness proofs are generalizations of those found in propositional and first-order hybrid logic, and 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.
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DOI 10.1007/s10992-012-9260-4
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References found in this work BETA

Generalized Quantifiers and Natural Language.John Barwise & Robin Cooper - 1981 - Linguistics and Philosophy 4 (2):159--219.
Generalized Quantifiers and Natural Language.Jon Barwise - 1980 - Linguistics and Philosophy 4:159.
First-Order Modal Logic.Roderic A. Girle, Melvin Fitting & Richard L. Mendelsohn - 2002 - Bulletin of Symbolic Logic 8 (3):429.
Combining Montague Semantics and Discourse Representation.Reinhard Muskens - 1996 - Linguistics and Philosophy 19 (2):143 - 186.

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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.
Hybrid Logic as Extension of Modal and Temporal Logic.Daniel Álvarez Domínguez - 2019 - Revista de Humanidades de Valparaíso 13:34-67.

View all 6 citations / Add more citations

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