Rigid First-Order Hybrid Logic

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

Publikation: Bidrag til bog/antologi/rapportKonferencebidrag i proceedingsForskningpeer review

Resumé

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.
OriginalsprogEngelsk
TitelLogic, Language, Information, and Computation : 26th International Workshop, WoLLIC 2019, Utrecht, The Netherlands, July 2-5, 2019, Proceedings
RedaktørerRosalie Lemhoff, Michael Moortgat, Ruy de Queiroz
Antal sider17
Udgivelses stedBerlin
ForlagSpringer
Publikationsdato2 jul. 2019
Sider53-69
ISBN (Trykt)978-366-259-5329
StatusUdgivet - 2 jul. 2019
NavnLecture Notes in Computer Science
Vol/bind11541
ISSN0302-9743

Citer dette

Blackburn, P. R., Martins, M., Manzano, M., & Huertas, A. (2019). Rigid First-Order Hybrid Logic. I R. Lemhoff, M. Moortgat, & R. de Queiroz (red.), Logic, Language, Information, and Computation: 26th International Workshop, WoLLIC 2019, Utrecht, The Netherlands, July 2-5, 2019, Proceedings (s. 53-69). Berlin: Springer. Lecture Notes in Computer Science, Bind. 11541
Blackburn, Patrick Rowan ; Martins, Manuel ; Manzano, Maria ; Huertas, Antonia . / Rigid First-Order Hybrid Logic. Logic, Language, Information, and Computation: 26th International Workshop, WoLLIC 2019, Utrecht, The Netherlands, July 2-5, 2019, Proceedings. red. / Rosalie Lemhoff ; Michael Moortgat ; Ruy de Queiroz. Berlin : Springer, 2019. s. 53-69 (Lecture Notes in Computer Science, Bind 11541).
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title = "Rigid First-Order Hybrid Logic",
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.",
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Blackburn, PR, Martins, M, Manzano, M & Huertas, A 2019, Rigid First-Order Hybrid Logic. i R Lemhoff, M Moortgat & R de Queiroz (red), Logic, Language, Information, and Computation: 26th International Workshop, WoLLIC 2019, Utrecht, The Netherlands, July 2-5, 2019, Proceedings. Springer, Berlin, Lecture Notes in Computer Science, bind 11541, s. 53-69.

Rigid First-Order Hybrid Logic. / Blackburn, Patrick Rowan; Martins, Manuel; Manzano, Maria ; Huertas, Antonia .

Logic, Language, Information, and Computation: 26th International Workshop, WoLLIC 2019, Utrecht, The Netherlands, July 2-5, 2019, Proceedings. red. / Rosalie Lemhoff; Michael Moortgat; Ruy de Queiroz. Berlin : Springer, 2019. s. 53-69 (Lecture Notes in Computer Science, Bind 11541).

Publikation: Bidrag til bog/antologi/rapportKonferencebidrag i proceedingsForskningpeer review

TY - GEN

T1 - Rigid First-Order Hybrid Logic

AU - Blackburn, Patrick Rowan

AU - Martins, Manuel

AU - Manzano, Maria

AU - Huertas, Antonia

PY - 2019/7/2

Y1 - 2019/7/2

N2 - 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.

AB - 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.

KW - Hybrid logic

KW - Rigidty

KW - Actualist semantics

KW - First-order modal logic

KW - Rigid predicate symbols

KW - Function symbols

KW - Varying domains

KW - Henkin models

M3 - Article in proceedings

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BT - Logic, Language, Information, and Computation

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A2 - de Queiroz, Ruy

PB - Springer

CY - Berlin

ER -

Blackburn PR, Martins M, Manzano M, Huertas A. Rigid First-Order Hybrid Logic. I Lemhoff R, Moortgat M, de Queiroz R, red., Logic, Language, Information, and Computation: 26th International Workshop, WoLLIC 2019, Utrecht, The Netherlands, July 2-5, 2019, Proceedings. Berlin: Springer. 2019. s. 53-69. (Lecture Notes in Computer Science, Bind 11541).