Abstract
In the previous chapters we have proved that the tree-hypersequent calculi are sound and complete with respect to their corresponding Hilbert systems, and that they are cut-free. All the proofs were developed in a purely syntactic fashion. In this chapter we tackle the same issues from a semantic point of view, giving alternative (though less constructive) proofs. This operation can shed further light on the tree-hypersequent calculi.
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References
K. Brünnler. Deep sequent systems for modal logic. In G. Governatori, I. Hodkinson, and Y. Venema, editors, Advances in Modal Logic, Vol 6, pp. 107–119. College Publications, London, 2006.
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Poggiolesi, F. (2010). Semantic Adequacy. In: Gentzen Calculi for Modal Propositional Logic. Trends in Logic, vol 32. Springer, Dordrecht. https://doi.org/10.1007/978-90-481-9670-8_8
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DOI: https://doi.org/10.1007/978-90-481-9670-8_8
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