Synthetic Completeness Proofs for Seligman-style Tableau Systems

Klaus Frovin Jørgensen, Patrick Rowan Blackburn, Thomas Bolander, Torben Braüner

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Abstract

Hybrid logic is a form of modal logic which allows reference to worlds. We can think of it as ‘modal logic with labelling built into the object language’ and various forms of labelled deduction have played a central role in its proof theory. Jerry Seligman’s work [11,12] in which ‘rules involving labels’ are rejected in favour of ‘rules for all’ is an interesting exception to this. Seligman’s approach was originally for natural deduction; the authors of the present paper recently extended it to tableau inference [1,2]. Our earlier work was syntactic: we showed completeness by translating between Seligman-style and labelled tableaus, but our results only covered the minimal hy- brid logic; in the present paper we provide completeness results for a wider range of hybrid logics and languages. We do so by adapting the synthetic approach to tableau completeness (due to Smullyan, and widely applied in modal logic by Fitting) so that we can directly build maximal consistent sets of tableau blocks.
Original languageEnglish
Title of host publicationProceedings of Advances in Modal Logic (AiML 2016)
Number of pages20
PublisherCollege Publications
Publication date2016
ISBN (Print)978-1-84890-201-5
Publication statusPublished - 2016
EventAdvances in Modal Logic 2016 - Eotovos University, Budapest, Hungary
Duration: 30 Aug 20162 Sep 2016

Conference

ConferenceAdvances in Modal Logic 2016
LocationEotovos University
CountryHungary
CityBudapest
Period30/08/201602/09/2016
SeriesAdvances in Modal Logic
Volume11

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