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\title{Epistemic Logic: Completeness of Modal Logics}
\author{Asta Halkjær From}
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\begin{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)~\cite{fagin1995}.
  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)~\cite{blackburn2001}.
\end{abstract}

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