Generalized Kripke semantics for the Lambek-Grishin calculus

@article{Chernilovskaya2012GeneralizedKS,
  title={Generalized Kripke semantics for the Lambek-Grishin calculus},
  author={Anna Chernilovskaya and Mai Gehrke and Lorijn van Rooijen},
  journal={Log. J. IGPL},
  year={2012},
  volume={20},
  pages={1110-1132}
}
properties. It turns out that this extension is precisely the algebra of Galois closed sets of the canonical frame as defined in section 2 of [Geh06]. Thus we get a simple abstract manner of working with the canonical frame. This makes it easy to treat additional operations and their interaction axioms. In particular, from A = (A,⊗, /, \,⊕,;, ) we get Aδ = (Aδ,⊗σ, / π, \ π,⊕π,; σ, σ) and Aδ is the algebra of Galois closed sets for some frame which we denote by (X,Y,6, R⊗σ , R⊕π) =: F(A). The… 

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