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.
- 15.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.Google Scholar