Hybrid Completeness

@article{Blackburn1998HybridC,
  title={Hybrid Completeness},
  author={Patrick Blackburn and Miroslava Tzakova},
  journal={Log. J. IGPL},
  year={1998},
  volume={6},
  pages={625-650}
}
In this paper we discuss two hybrid languages , L(∀) and L(↓), and provide them with complete axiomatizations. Both languages combine features of modal and classical logic. Like modal languages, they contain modal operators and have a Kripke semantics. Unlike modal languages, in these systems it is possible to ‘label’ states by using ∀ and ↓ to bind special state variables . This paper explores the consequences of hybridization for completeness. As we shall show, the challenge is to blend the… 

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