@INCOLLECTION{Schmidt98f, AUTHOR = {Schmidt, R. A.}, YEAR = {1998}, TITLE = {Resolution is a Decision Procedure for Many Propositional Modal Logics}, EDITOR = {Kracht, M. and de Rijke, M. and Wansing, H. and Zakharyaschev, M.}, BOOKTITLE = {Advances in Modal Logic, Volume 1}, SERIES = {Lecture Notes}, VOLUME = {87}, PUBLISHER = {CSLI Publications}, ADDRESS = {Stanford}, PAGES = {189--208}, URL = {http://www.cs.man.ac.uk/~schmidt/publications/Schmidt98f.html}, ISBN = {1-57586-103-8 (hardback), 1-57586-102-X (paper)}, ABSTRACT = {The paper shows satisfiability in many propositional modal systems, including \textit{K}, \textit{KD}, \textit{KT} and \textit{KB}, their combinations as well as their multi-modal versions, can be decided by ordinary resolution procedures. This follows from a general result that resolution and condensing is a decision procedure for the satisfiability problem of formulae in so-called \emph{path logics}. Path logics arise from propositional and normal uni- and multi-modal logics by the \emph{optimised functional translation} method. The decision result provides an alternative decision proof for the relevant modal systems, and related systems in artificial intelligence. However, this alone is not very interesting. A more far-reaching consequence of the result has practical value, namely, any standard first-order theorem prover that is based on resolution can serve as a reasonable and efficient inference tool for modal reasoning. }}