Hybrid logics with infinitary proof systems

We provide a strongly complete infinitary proof system for hybrid logic. This proof system can be extended with countably many sequents. Thus, although these logics may be non-compact, strong completeness proofs are provided for infinitary hybrid versions of non-compact logics like ancestral logic and Segerberg’s modal logic with the bounded chain condition. This extends the completeness result for hybrid logics by Gargov, Passy, and Tinchev
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