Tableaux for quantified hybrid logic

Patrick Blackburn, Maarten Marx

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

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 □ and ◊ modalities it contains names for (and variables over) states, operators @s for asserting that a formula holds at a named state, and a binder ↓ 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).

Original languageEnglish
Title of host publicationAutomated Reasoning with Analytic Tableaux and Related Methods : International Conference, TABLEAUX 2002, Proceedings
EditorsUwe Egly, Christian G. Fermuller
Number of pages15
PublisherSpringer
Publication date2002
Pages38-52
ISBN (Print)3540439293, 9783540439295
ISBN (Electronic)978-3-540-45616-2
DOIs
Publication statusPublished - 2002
Externally publishedYes
EventInternational Conference on Automated Reasoning with Analytic Tableaux and Related Methods, TABLEAUX 2002 - Copenhagen, Denmark
Duration: 30 Jul 20021 Aug 2002

Conference

ConferenceInternational Conference on Automated Reasoning with Analytic Tableaux and Related Methods, TABLEAUX 2002
Country/TerritoryDenmark
CityCopenhagen
Period30/07/200201/08/2002
SponsorKurt Godel Society, Vienna University of Technoloy
SeriesLecture Notes in Computer Science
Volume2381
ISSN0302-9743

Keywords

  • Modal Logic
  • Hybrid Logic
  • Replacement Rule
  • Predicate Abstraction
  • Conjunctive Rule

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