Abstract: Described herein is a composition including a substantially potash-free hydraulic cementitious material and at least one polyol compound having an acyclic polyhydroxy backbone chain comprising four or five adjacent carbon atoms, wherein a hydroxyl group is attached to each carbon of the backbone chain, and wherein the composition includes an effective amount of at least one calcium silicate or calcium aluminate material in a crystalline phase. Also described herein is a composition including a substantially calcium hydroxide-free hydraulic cementitious material and at least one polyol compound having an acyclic polyhydroxy backbone chain comprising four or five adjacent carbon atoms, wherein a hydroxyl group is attached to each carbon of the backbone chain, and wherein the composition includes at least one alkali-activated binder. Also described herein are methods and admixtures for increasing the strength of a hydraulic cementitious material.