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\begin{document}

\title{Formalizing a Seligman-Style Tableau System for Hybrid Logic}
\author{Asta Halkjær From}
\maketitle

\begin{abstract}
This work is a formalization of soundness and completeness proofs
for a Seligman-style tableau system for hybrid logic. The completeness
result is obtained via a synthetic approach using maximally
consistent sets of tableau blocks. The formalization differs from
previous work~\cite{jlog17, aiml16} in a few ways. First, to avoid the need to backtrack in
the construction of a tableau, the formalized system has no unnamed
initial segment, and therefore no Name rule. Second, I show that the
full Bridge rule is admissible in the system. Third, I start from rules
restricted to only extend the branch with new formulas, including only
witnessing diamonds that are not already witnessed, and show that
the unrestricted rules are admissible. Similarly, I start from simpler
versions of the @-rules and show that these are sufficient.
The GoTo rule is restricted using a notion of potential such that each
application consumes potential and potential is earned through applications of
the remaining rules. I show that if a branch can be closed then it can
be closed starting from a single unit. Finally, Nom is restricted by
a fixed set of allowed nominals. The resulting system should be terminating.
\end{abstract}

\section*{Preamble}

The formalization was part of the author's MSc thesis in Computer Science and Engineering at the Technical University of Denmark (DTU).

\paragraph{Supervisors:}

\begin{itemize}
  \item Jørgen Villadsen
  \item Alexander Birch Jensen (co-supervisor)
  \item Patrick Blackburn (Roskilde University, external supervisor)
\end{itemize}

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