### 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.

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 language | English |
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Title of host publication | Volume of abstracts : Non-classical Modal and Predicate Logics |

Editors | Petr Cintula, Shier Ju, Martin Víta |

Place of Publication | Prague |

Publisher | F solutions |

Publication date | 2011 |

Pages | 35-41 |

ISBN (Print) | 987-80-87465-00-4 |

Publication status | Published - 2011 |

Event | Non-classical Modal and Predicate Logics 2011 - Guangzhou, Canton, China Duration: 5 Dec 2011 → 9 Dec 2011 |

### Conference

Conference | Non-classical Modal and Predicate Logics 2011 |
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Country | China |

City | Guangzhou, Canton |

Period | 05/12/2011 → 09/12/2011 |

### Cite this

Braüner, T. (2011). First-Order Hybrid Logic: Introduction and Survey. In P. Cintula, S. Ju, & M. Víta (Eds.),

*Volume of abstracts: Non-classical Modal and Predicate Logics*(pp. 35-41). Prague: F solutions.