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http://hdl.handle.net/10773/26443
Title: | Rigid first-order hybrid logic |
Author: | Blackburn, Patrick Martins, Manuel A. Manzano, María Huertas, Antonia |
Keywords: | Hybrid logic First-order modal logic Rigidity Rigid predicate symbols Function symbols Varying domains Actualist semantics Henkin models |
Issue Date: | Jun-2019 |
Publisher: | Springer Verlag |
Abstract: | Hybrid logic is usually viewed as a variant of modal logic in which it is possible to refer to worlds. But when one moves beyond propositional hybrid logic to first- or higher-order hybrid logic, it becomes useful to view it as a systematic modal language of rigidification. The key point is this: @ can be used to rigidify not merely formulas, but other types of symbol as well. This idea was first explored in first-order hybrid logic (without function symbols) where @ was used to rigidify the firstorder constants. It has since been used in hybrid type-theory: here one only has function symbols, but they are of every finite type, and @ can rigidify any of them. This paper fills the remaining gap: it introduces a first-order hybrid language which handles function symbols, and allows predicate symbols to be rigidified. The basic idea is straightforward, but there is a slight complication: transferring information about rigidity between the level of terms and formulas. We develop a syntax to deal with this, provide an axiomatization, and prove a strong completeness result for a varying domain (actualist) semantics. |
Peer review: | yes |
URI: | http://hdl.handle.net/10773/26443 |
DOI: | 10.1007/978-3-662-59533-6_4 |
ISBN: | 978-3-662-59532-9 |
ISSN: | 0302-9743 |
Appears in Collections: | CIDMA - Capítulo de livro AGG - Capítulo de livro |
Files in This Item:
File | Description | Size | Format | |
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FO_HL_rigid.pdf | 355.82 kB | Adobe PDF | View/Open |
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