The Two-Variable Guarded Fragment with Transitive Guards Is 2EXPTIME-Hard [chapter]

Emanuel Kieroński
2003 Lecture Notes in Computer Science  
We prove that the satisfiability problem for the two-variable guarded fragment with transitive guards GF 2 + T G is 2EXPTIME-hard. This result closes the open questions left in [4] , [17] . In fact, we show 2EXPTIME-hardness of minGF 2 + T G, a fragment of GF 2 + T G without equality and with just one transitive relation ≺, which is the only non-unary symbol allowed. Our lower bound for minGF 2 + T G matches the upper bound for the whole guarded fragment with transitive guards and the
more » ... ed number of variables GF + T G given by Szwast and Tendera [17], so in fact GF 2 + T G is 2EXPTIME-complete. It is surprising that the complexity of minGF 2 + T G is higher then the complexity of the variant with one-way transitive guards GF 2 + −→ T G [9]. The latter logic appears naturally as a counterpart of temporal logics without past operators.
doi:10.1007/3-540-36576-1_19 fatcat:i4iolnu5arhxfme3satc5qyvbu