PP-2003-10:
Blackburn, Patrick and Marx, Maarten
(2003)
*Tableaux for Quantified Hybrid Logic.*
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## Abstract

We present a (sound and complete) tableau calculus for Quantified

Hybrid Logic (QHL). QHL is an extension of orthodox quantified modal

logic: as well as the usual Box and Diamond modalities it contains

names for (and variables over) states, operators @_s for asserting

that a formula holds at a named state, and a binder downarrow that

binds a variable to the current state. The first-order component

contains equality and rigid and non-rigid designators. As far as we

are aware, ours is the first tableau system for QHL.

Completeness is established via a variant of the standard translation

to first-order logic. More concretely, a valid QHL-sentence is

translated into a valid first-order sentence in the correspondence

language. As it is valid, there exists a first-order tableau proof for

it. This tableau proof is then converted into a QHL tableau proof for

the original sentence. In this way we recycle a well-known result

(completeness of first-order logic) instead of a well-known proof.

The tableau calculus is highly flexible. We only present it for the

constant domain semantics, but slight changes render it complete for

varying, expanding or contracting domains. Moreover, completeness with

respect to specific frame classes can be obtained simply by adding

extra rules or axioms (this can be done for every first-order

definable class of frames which is closed under and reflects generated

subframes).

Item Type: | Report |
---|---|

Report Nr: | PP-2003-10 |

Series Name: | Prepublication (PP) Series |

Year: | 2003 |

Uncontrolled Keywords: | hybrid logic, first order modal logic, tableaux |

Subjects: | Logic |

Date Deposited: | 12 Oct 2016 14:36 |

Last Modified: | 12 Oct 2016 14:36 |

URI: | https://eprints.illc.uva.nl/id/eprint/94 |

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