I feel like I kind of know this, but sometimes I feel unsure. It's pretty similar to the Swedish sin, sitt. Is there a good rule or a nice, short explanation for when and where to use si, sia instead of li, sxi?
Use si or sia when referring to the already-introduced subject of the sentence:
- La virino rigardis la bildon antaŭ si -> "The woman looked at the picture in front of her", the picture is in front of the subject of the sentence ("the woman")
- Li eniris sian domon -> "He entered his (own) house", the house belongs to the subject of the sentence ("he")
- La infano amas sian patrinon -> "The child loves its (own) mother", the mother belongs to the subject of the sentence ("the child")
You asked for short:
Use si/sia when both are true
- the pronoun is not part of the subject.
- the pronoun refers to the subject of the verb.
Regarding point 1: you'll never see la viro kaj sia edzino estas... because lia edzino is part of the subject.
Regarding point 2: it's important to notice that it's the subject of the verb and not the subject of the sentence, because while they're usually the same, they are not always the same.
- Mi vidis lin bati sin (the guy hit himself.)