A tableau calculus with automaton-labelled formulae for regular grammar logics
| Abstract |
We present a sound and complete tableau calculus for the class of regular grammar logics. Our tableau rules use a special feature called automaton-labelled formulae, which are similar to formulae of automaton propositional dynamic logic. Our calculus is cut-free and has the analytic superformula property so it gives a decision procedure. We show that the known EXPTIME upper bound for regular grammar logics can be obtained using our tableau calculus. We also give an effective Craig interpolation lemma for regular grammar logics using our calculus.
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References found in this work BETA
Modal Tableau Calculi and Interpolation.Wolfgang Rautenberg - 1983 - Journal of Philosophical Logic 12 (4):403 - 423.
An Overview of Tableau Algorithms for Description Logics.Franz Baader & Ulrike Sattler - 2001 - Studia Logica 69 (1):5-40.
EXPtime Tableaux for ALC.Francesco M. Donini & Fabio Massacci - 2000 - Artificial Intelligence 124 (1):87-138.
Analytic Tableau Systems and Interpolation for the Modal Logics KB, KDB, K5, KD.Linh Anh Nguyen - 2001 - Studia Logica 69 (1):41-57.
Citations of this work BETA
Grammar Logics in Nested Sequent Calculus: Proof Theory and Decision Procedures.Alwen Tiu, Egor Ianovski & Rajeev Goré - 2012 - In Thomas Bolander, Torben Braüner, Silvio Ghilardi & Lawrence Moss (eds.), Advances in Modal Logic, Volume 9. CSLI Publications. pp. 516-537.
ExpTime Tableau Decision Procedures for Regular Grammar Logics with Converse.Linh Anh Nguyen & Andrzej Szałas - 2011 - Studia Logica 98 (3):387-428.
Modal Logics for Reasoning About Infinite Unions and Intersections of Binary Relations.Natasha Alechina, Philippe Balbiani & Dmitry Shkatov - 2012 - Journal of Applied Non-Classical Logics 22 (4):275 - 294.
Constructing Finite Least Kripke Models for Positive Logic Programs in Serial Regular Grammar Logics.Linh Nguyen - 2008 - Logic Journal of the IGPL 16 (2):175-193.
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