Decidability for Justification Logics Revisited

TitleDecidability for Justification Logics Revisited
Publication TypeBook Chapter
Year of Publication2013
AuthorsBucheli, S, Kuznets, R, Studer, T
EditorBezhanishvili, G, Löbner, S, Marra, V, Richter, F
Book TitleLogic, Language, and Computation, 9th International Tbilisi Symposium on Logic, Language, and Computation, TbiLLC 2011, Kutaisi, Georgia, September 26-30, 2011, Revised Selected Papers
Keywordsdecidability, filtration, justification logic
AbstractJustification logics are propositional modal-like logics that instead of statements \emph{$A$ is known} include statements of the form \emph{$A$ is known for reason $t$} where the term $t$ can represent an informal justification for $A$ or a formal proof of $A$. In our present work, we introduce model-theoretic tools, namely: filtrations and a certain form of generated submodels, in the context of justification logic in order to obtain decidability results. Apart from reproving already known results in a uniform way, we also prove new results. In particular, we use our submodel construction to establish decidability for a justification logic with common knowledge for which so far no decidability proof was available.