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We extend the mono-modal CEGAR-tableaux of Goré and Kikkert to normal multi-modal logic \(\textrm{K}_{\textrm{n}}\)  with global assumptions. We then extend these CEGAR-tableaux to multi-modal tense logic \(\textrm{Kt}_{\textrm{n}}\) without global assumptions by “compiling in” the residuation conditions between “future” and “past” modalities. Our new implementation CEGARBox++ uses \(\mathrm {C^{++}}\) and includes multiple optimisations which speed up proof-search. \(\texttt {CEGARBox++}\) is the best satisfiability-checker for mono-modal tense logic \(\textrm{Kt}_{\textrm{1}}\) but is not competitive for global assumptions.

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Improved Decision Procedures for Multi-modal Tense Logic Using CEGAR-Tableaux

  • 会议论文

  • 出版模式：

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  • 发表日期：

    2026年

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  • Rajeev Goré,
  • Cormac Kikkert

摘要

We extend the mono-modal CEGAR-tableaux of Goré and Kikkert to normal multi-modal logic \(\textrm{K}_{\textrm{n}}\)  with global assumptions. We then extend these CEGAR-tableaux to multi-modal tense logic \(\textrm{Kt}_{\textrm{n}}\) without global assumptions by “compiling in” the residuation conditions between “future” and “past” modalities. Our new implementation CEGARBox++ uses \(\mathrm {C^{++}}\) and includes multiple optimisations which speed up proof-search. \(\texttt {CEGARBox++}\) is the best satisfiability-checker for mono-modal tense logic \(\textrm{Kt}_{\textrm{1}}\) but is not competitive for global assumptions.