In this game of Rock, Paper, Scissors, you have 4 signs: Sun, Moon, Star, Planet. You also have twin versions of these signs.
Sun is stronger than Moon.
Moon is stronger than Star.
Star is stronger than Sun.
Stronger signs from these three deal 20% more damage against the weaker sign, while the weaker deals 20% less damage. If the attacker is a double sign, the damage modifier becomes 30%.
In other words: Sun deals 20% damage against double Moon, but double Moon deals 30% less damage against Sun.
Double Planet has a +10% damage bonus against all three, while a single Planet has a 50% damage bonus against double Planet, while doing normal damage to all other signs.
There are also resistance bonuses for Sun, Moon, and Star, and XP bonuses for Planets:
Sun: +5% to fire attacks and sleep
Double Sun: +10% to fire attack and sleep
Star: +5% to storm attacks and poison
Double Star: +10% to storm attacks and poison
Moon: +5% to water attacks and confusion
Double Moon: +10% to water attacks and confusion
Planet: +5% XP bonus
Double Planet: +10% XP bonus
Sources: GamesRadar and Prima Games