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.

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

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.”