@INPROCEEDINGS{GorankoHustadtSchmidtVakarelov04a, AUTHOR = {Goranko, V. and Hustadt, U. and Schmidt, R. A. and Vakarelov, D.}, YEAR = {2004}, TITLE = {{SCAN} is Complete for All {S}ahlqvist Formulae}, EDITOR = {Berghammer, R. and M{\"o}ller, B. and Struth, G.}, BOOKTITLE = {Relational and {K}leene-Algebraic Methods in Computer Science (RelMiCS 7)}, SERIES = {Lecture Notes in Computer Science}, VOLUME = {3051}, PUBLISHER = {Springer}, PAGES = {149--162}, URL = {\url{http://www.cs.man.ac.uk/~schmidt/publications/GorankoHustadtSchmidtVakarelov04a.html}}, ABSTRACT = { SCAN is an algorithm for reducing monadic existential second-order logic formulae to equivalent simpler formulae, often first-order logic formulae. It is provably impossible for such a reduction to first-order logic to be always successful, even if there is an equivalent first-order formula for a second-order logic formula. In this paper we show that SCAN successfully computes the first-order equivalents of all Sahlqvist formulae in the classical (multi-)modal language. } }