Axiomatizing Epistemic Logic of Friendship via Tree Sequent Calculus

Katsuhiko Sano

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arXiv · 1704.07149

Axiomatizing Epistemic Logic of Friendship via Tree Sequent Calculus

Katsuhiko Sano

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Abstract

This paper positively solves an open problem if it is possible to provide a Hilbert system to Epistemic Logic of Friendship (EFL) by Seligman, Girard and Liu. To find a Hilbert system, we first introduce a sound, complete and cut-free tree (or nested) sequent calculus for EFL, which is an integrated combination of Seligman's sequent calculus for basic hybrid logic and a tree sequent calculus for modal logic. Then we translate a tree sequent into an ordinary formula to specify a Hilbert system of EFL and finally show that our Hilbert system is sound and complete for the intended two-dimensional semantics.

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Katsuhiko Sano. 2017-04-24. Axiomatizing Epistemic Logic of Friendship via Tree Sequent Calculus. https://arxiv.org/abs/1704.07149

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