The generalized LR parsing algorithm for context-free grammars, invented by Tomita in 1986, is extended for the case of Boolean grammars, which are a recently introduced generalization of context-free grammars with logical connectives added to the formalism of rules. In addition to the standard LR operations, Shift and Reduce, the new algorithm uses a third operation called Invalidate, which reverses a previously made reduction; this makes the algorithm considerably different from its prototype, though it can still be made to work in time O(n³).