PP200310: Blackburn, Patrick and Marx, Maarten (2003) Tableaux for Quantified Hybrid Logic. [Report]

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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 firstorder component contains equality and rigid and nonrigid 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 firstorder logic. More concretely, a valid QHLsentence is translated into a valid firstorder sentence in the correspondence language. As it is valid, there exists a firstorder 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 wellknown result (completeness of firstorder logic) instead of a wellknown 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 firstorder definable class of frames which is closed under and reflects generated subframes).
Item Type:  Report 

Report Nr:  PP200310 
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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