# Epistemic Logic: Completeness of Modal Logics

 Title: Epistemic Logic: Completeness of Modal Logics Author: Asta Halkjær From Submission date: 2018-10-29 Abstract: This work is a formalization of epistemic logic with countably many agents. It includes proofs of soundness and completeness for the axiom system K. The completeness proof is based on the textbook "Reasoning About Knowledge" by Fagin, Halpern, Moses and Vardi (MIT Press 1995). The extensions of system K (T, KB, K4, S4, S5) and their completeness proofs are based on the textbook "Modal Logic" by Blackburn, de Rijke and Venema (Cambridge University Press 2001). Papers: https://doi.org/10.1007/978-3-030-88853-4_1, https://doi.org/10.1007/978-3-030-90138-7_2. Change history: [2021-04-15]: Added completeness of modal logics T, KB, K4, S4 and S5. BibTeX: @article{Epistemic_Logic-AFP, author = {Asta Halkjær From}, title = {Epistemic Logic: Completeness of Modal Logics}, journal = {Archive of Formal Proofs}, month = oct, year = 2018, note = {\url{https://isa-afp.org/entries/Epistemic_Logic.html}, Formal proof development}, ISSN = {2150-914x}, } License: BSD License Used by: Public_Announcement_Logic Status: [ok] This is a development version of this entry. It might change over time and is not stable. Please refer to release versions for citations.