diff --git a/thys/Hybrid_Logic/document/root.tex b/thys/Hybrid_Logic/document/root.tex --- a/thys/Hybrid_Logic/document/root.tex +++ b/thys/Hybrid_Logic/document/root.tex @@ -1,91 +1,92 @@ \documentclass[11pt,a4paper]{article} +\usepackage[utf8]{inputenc} \usepackage{isabelle,isabellesym} % further packages required for unusual symbols (see also % isabellesym.sty), use only when needed \usepackage{amssymb} %for \, \, \, \, \, \, %\, \, \, \, \, %\, \, \ %\usepackage{eurosym} %for \ %\usepackage[only,bigsqcap]{stmaryrd} %for \ %\usepackage{eufrak} %for \ ... \, \ ... \ (also included in amssymb) %\usepackage{textcomp} %for \, \, \, \, \, %\ % this should be the last package used \usepackage{pdfsetup} % urls in roman style, theory text in math-similar italics \urlstyle{rm} \isabellestyle{it} % for uniform font size %\renewcommand{\isastyle}{\isastyleminor} \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~\cite{jlog17}. The completeness result is obtained via a synthetic approach using maximally consistent sets of tableau blocks~\cite{aiml16}. The formalization differs from the cited work 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 \textit{Name} rule. Second, I show that the full \textit{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 derivable. Similarly, I start from simpler versions of the \( @ \)-rules and derive the general ones. Finally, the \textit{GoTo} rule is restricted using a notion of coins such that each application consumes a coin and coins are 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 coin. These restrictions are imposed to rule out some means of nontermination~\cite{jlog17}. \end{abstract} \section*{Preamble} The formalization is 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} \newpage \tableofcontents \newpage % sane default for proof documents \parindent 0pt\parskip 0.5ex % generated text of all theories \input{session} \nocite{*} % optional bibliography \bibliographystyle{abbrv} \bibliography{root} \addcontentsline{toc}{section}{References} \end{document} %%% Local Variables: %%% mode: latex %%% TeX-master: t %%% End: