Titlebook: Automated Reasoning; 12th International J Christoph Benzmüller,Marijn J.H. Heule,Renate A. S Conference proceedings‘‘‘‘‘‘‘‘ 2024 The Editor

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https://doi.org/10.1007/978-1-0716-3690-9o an unblocked phase, where any rule can be backward applied, and a blocked phase where only right rules can be used. We prove that, if proof search for a sequent . in . fails, then a Kripke countermodel for . can be constructed.

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A Cyclic Proof System for?Guarded Kleene Algebra with?Tests . allows for a non-well-founded sequent system whose set of regular proofs is complete with respect to the guarded language model. This is unlike the situation with Kleene Algebra, where hypersequents are required. Moreover, the decision procedure induced by proof search runs in ., whereas that of Kleene Algebra is in ..

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0302-9743 Calculi, Proof Theory and Decision Procedures; and Unification, Rewriting and Computational Models...This book is open access...?.978-3-031-63500-7978-3-031-63501-4Series ISSN 0302-9743 Series E-ISSN 1611-3349

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https://doi.org/10.1007/978-1-0716-3690-9 a ‘certificate’ for satisfiable modal formulae that can be independently checked to assure a user that the result of . is correct. This complements the existing provision of proofs for unsatisfiable modal formulae.

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