We report ab initio calculations of features of the potential energy surfaces for two reactions of potential importance for the combustion of boron in fluorine-containing environments; HF+HOBO-->H2O+FBO and HF+OBBO-->FBO+HBO. Both reactions proceed through four-center transition states and yield the product FBO, a stable molecule that appears to play a similar role for B/F/O/H combustion as the isoelectronic CO2 does for hydrocarbon combustion. Multireference configuration interaction calculations with valence triple-zeta, double polarization; basis sets yield energy barriers of 27.2 and 46.2 kcal/mol, respectively, for these two reactions. Transition state theory calculations based on the ab initio potential energy surface information yield the following three-parameter fits for the temperature-dependent rate coefficients. k(HOBO)(T)=1.436x10(2) T(2.71)exp(-11917/T) cm(3)/mol s and k(OBBO)(T)=4.819x10(4) T(2.38)exp(-22028/T) cm(3)/mol s. Both reactions are predicted to be orders of magnitude slower than the estimated rates used lh recent combustion modeling efforts.