First-Order Hybrid Logic: Introduction and Survey

Research output: Contribution to journalJournal articleResearchpeer-review

Abstract

Hybrid logic is an extension of modal logic which allows us to refer explicitly to points of the model in the syntax of formulas. It is easy to justify interest in hybrid logic on applied grounds, with the usefulness of the additional expressive power. For example, when reasoning about time one often wants to build up a series of assertions about what happens at a particular instant, and standard modal formalisms do not allow this. What is less obvious is that the route hybrid logic takes to overcome this problem often actually improves the behaviour of the underlying modal formalism. For example, it becomes far simpler to formulate proof-systems for hybrid logic, and completeness results can be proved of a generality that is simply not available in modal logic. That is, hybridization is a systematic way of remedying a number of known deficiencies of modal logic. First-order hybrid logic is obtained by adding first-order machinery to propositional hybrid logic, or equivalently, by adding hybrid-logical machinery to first-order modal logic. In this short paper we introduce first-order hybrid logic and we give a survey of work in the area.
Original languageEnglish
JournalLogic Journal of the IGPL
Volume22
Issue number1
Pages (from-to)155-165
ISSN1367-0751
DOIs
Publication statusPublished - 2014

Keywords

  • Hybrid logic
  • first-order logic

Cite this

@article{6319cd1674f1410b99172680e47423eb,
title = "First-Order Hybrid Logic: Introduction and Survey",
abstract = "Hybrid logic is an extension of modal logic which allows us to refer explicitly to points of the model in the syntax of formulas. It is easy to justify interest in hybrid logic on applied grounds, with the usefulness of the additional expressive power. For example, when reasoning about time one often wants to build up a series of assertions about what happens at a particular instant, and standard modal formalisms do not allow this. What is less obvious is that the route hybrid logic takes to overcome this problem often actually improves the behaviour of the underlying modal formalism. For example, it becomes far simpler to formulate proof-systems for hybrid logic, and completeness results can be proved of a generality that is simply not available in modal logic. That is, hybridization is a systematic way of remedying a number of known deficiencies of modal logic. First-order hybrid logic is obtained by adding first-order machinery to propositional hybrid logic, or equivalently, by adding hybrid-logical machinery to first-order modal logic. In this short paper we introduce first-order hybrid logic and we give a survey of work in the area.",
keywords = "Hybrid logic, first-order logic, Hybrid logic, first-order logic",
author = "Torben Bra{\"u}ner",
year = "2014",
doi = "10.1093/jigpal/jzt039",
language = "English",
volume = "22",
pages = "155--165",
journal = "Logic Journal of the IGPL",
issn = "1367-0751",
publisher = "Oxford Academic",
number = "1",

}

First-Order Hybrid Logic: Introduction and Survey. / Braüner, Torben.

In: Logic Journal of the IGPL, Vol. 22, No. 1, 2014, p. 155-165.

Research output: Contribution to journalJournal articleResearchpeer-review

TY - JOUR

T1 - First-Order Hybrid Logic: Introduction and Survey

AU - Braüner, Torben

PY - 2014

Y1 - 2014

N2 - Hybrid logic is an extension of modal logic which allows us to refer explicitly to points of the model in the syntax of formulas. It is easy to justify interest in hybrid logic on applied grounds, with the usefulness of the additional expressive power. For example, when reasoning about time one often wants to build up a series of assertions about what happens at a particular instant, and standard modal formalisms do not allow this. What is less obvious is that the route hybrid logic takes to overcome this problem often actually improves the behaviour of the underlying modal formalism. For example, it becomes far simpler to formulate proof-systems for hybrid logic, and completeness results can be proved of a generality that is simply not available in modal logic. That is, hybridization is a systematic way of remedying a number of known deficiencies of modal logic. First-order hybrid logic is obtained by adding first-order machinery to propositional hybrid logic, or equivalently, by adding hybrid-logical machinery to first-order modal logic. In this short paper we introduce first-order hybrid logic and we give a survey of work in the area.

AB - Hybrid logic is an extension of modal logic which allows us to refer explicitly to points of the model in the syntax of formulas. It is easy to justify interest in hybrid logic on applied grounds, with the usefulness of the additional expressive power. For example, when reasoning about time one often wants to build up a series of assertions about what happens at a particular instant, and standard modal formalisms do not allow this. What is less obvious is that the route hybrid logic takes to overcome this problem often actually improves the behaviour of the underlying modal formalism. For example, it becomes far simpler to formulate proof-systems for hybrid logic, and completeness results can be proved of a generality that is simply not available in modal logic. That is, hybridization is a systematic way of remedying a number of known deficiencies of modal logic. First-order hybrid logic is obtained by adding first-order machinery to propositional hybrid logic, or equivalently, by adding hybrid-logical machinery to first-order modal logic. In this short paper we introduce first-order hybrid logic and we give a survey of work in the area.

KW - Hybrid logic

KW - first-order logic

KW - Hybrid logic

KW - first-order logic

U2 - 10.1093/jigpal/jzt039

DO - 10.1093/jigpal/jzt039

M3 - Journal article

VL - 22

SP - 155

EP - 165

JO - Logic Journal of the IGPL

JF - Logic Journal of the IGPL

SN - 1367-0751

IS - 1

ER -