Rigid First-Order Hybrid Logic

Patrick Rowan Blackburn, Manuel Martins, Maria Manzano, Antonia Huertas

Research output: Chapter in Book/Report/Conference proceedingArticle in proceedingsResearchpeer-review

Abstract

Hybrid logic is usually viewed as a variant of modal logicin which it is possible to refer to worlds. But when one moves beyondpropositional hybrid logic to first or higher-order hybrid logic, it becomesuseful to view it as a systematicmodal language of rigidification.Thekeypoint is this: @ can be used to rigidify not merely formulas, but othertypes of symbol as well. This idea was first explored in first-order hybridlogic (without function symbols) where @ was used to rigidify the first-order constants. It has since been used in hybrid type-theory: here oneonly has function symbols, but they are of every finite type, and @ canrigidify any of them. This paper fills the remaining gap: it introduces afirst-order hybrid language which handles function symbols, and allowspredicate symbols to be rigidified. The basic idea is straightforward, butthere is a slight complication: transferring information about rigiditybetween the level of terms and formulas. We develop a syntax to dealwith this, provide an axiomatization, and prove a strong completenessresult for a varying domain (actualist) semantics.
Original languageEnglish
Title of host publicationLogic, Language, Information, and Computation : 26th International Workshop, WoLLIC 2019, Utrecht, The Netherlands, July 2-5, 2019, Proceedings
EditorsRosalie Lemhoff, Michael Moortgat, Ruy de Queiroz
Number of pages17
Place of PublicationBerlin
PublisherSpringer
Publication date2 Jul 2019
Pages53-69
ISBN (Print)978-366-259-5329
DOIs
Publication statusPublished - 2 Jul 2019
Event26th Workshop on Logic, Language, Information and Computation - Utrecht University, Utrecht, Netherlands
Duration: 2 Jul 20195 Jul 2019
https://wollic2019.sites.uu.nl/

Workshop

Workshop26th Workshop on Logic, Language, Information and Computation
LocationUtrecht University
CountryNetherlands
CityUtrecht
Period02/07/201905/07/2019
Internet address
SeriesLecture Notes in Computer Science
Volume11541
ISSN0302-9743

Keywords

  • Hybrid logic
  • Rigidty
  • Actualist semantics
  • First-order modal logic
  • Rigid predicate symbols
  • Function symbols
  • Varying domains
  • Henkin models

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