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Title: Rigid first-order hybrid logic
Author: Blackburn, Patrick
Martins, Manuel
Manzano, María
Huertas, Antonia
Keywords: Hybrid logic
First-order modal logic
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
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

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