Axiomatizing Epistemic Logic of Friendship via Tree Sequent Calculus
Logic in Computer Science
2019-07-11 v3 Logic
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.
Keywords
Cite
@article{arxiv.1704.07149,
title = {Axiomatizing Epistemic Logic of Friendship via Tree Sequent Calculus},
author = {Katsuhiko Sano},
journal= {arXiv preprint arXiv:1704.07149},
year = {2019}
}
Comments
24 pages, 1 figure