@INPROCEEDINGS{GanzingerMeyerVeanes-99-lics,
       AUTHOR = {Ganzinger, H. and Meyer, Chr. and Veanes, M.},
       TITLE = {The Two-Variable Guarded Fragment with Transitive Relations},
       YEAR = {1999},
        BOOKTITLE          = {Proc.\ 14th IEEE Symposium on Logic in Computer Science},
	PAGES		   = {24--34},
 	PUBLISHER          = {IEEE Computer Society Press},
       ABSTRACT = {
We consider the restriction of the guarded fragment
to the two-variable case where, in addition, binary relations
may be specified as transitive.
We show that (i) this very restricted form of the guarded fragment 
without equality is undecidable and that (ii) when
allowing transitive relations other than equality to
occur only in guards, the logic becomes decidable.
The latter subclass of the guarded fragment
is the one that occurs naturally when translating multi-modal
logics of the type K4, S4 or S5 into first-order logic.
We also show that the loosely guarded fragment 
with a single transitive relation
is undecidable.
},
       URL = {\hgURL{~hg/pca.html#99LICS.1}}
}