I'm asking this in the context of a logical programming language similar to Prolog.
Say I have the rule $P ⇒ (Q ∨ S)$ . How would I go about proving the truth value of $Q$, assuming I know the values of $S$ and $P$, and possibly other information.
I've thought about it and found that I could prove that $Q$ is True for $(P ∧ ¬S)$ , in other words $Q$ must be True if $P$ is True and $S$ is False. However I can't seem to figure out what to do if $S$ is True.
Any help is appreciated !
edit : thanks @ervx for pointing out $P ⇒ Q ∨ S$ vs $P ⇒ (Q ∨ S)$