That's where move descriptions come in to play.Nice idea, and the only way i can see dual-typed moves being a real thing. Let's not forget that Pokemon is a kid's game mainly, and there is no way that GF would introduce moves that are difficult for kids to figure out their effectiveness against other types.
"a mysterious Ice attack that deals damage like a Fire attack" would be an example of this. Kids might start to connect the dots when they see that it's innefective to Rock Pokemon like other Ice techniques and so on