Grell Philosopher causes Horrors to gain only activated abilities. They don't gain keyword abilities (unless those keyword abilities are activated), triggered abilities, or static abilities.

The granted abilities effectively use “this permanent” rather than “[that card's name],” so you treat the abilities as if they were printed on the creature that gained the ability. For example, say the artifact was Universal Solvent, which has the ability “{7}, {T}, Sacrifice Universal Solvent: Destroy target permanent.” If Grell Philosopher gained that ability, you'd treat it as though it said “{7}, {T}, Sacrifice Grell Philosopher: Destroy target permanent.”

Activated abilities contain a colon. They're generally written “[Cost]: [Effect].” Some keywords are activated abilities and will have colons in their reminder text.