Ternary Logic I

Alice stumbles into a garden where she comes across a strange looking man with writhing multicoloured hair, which is tied back in a braid with three strands.
Had Matter: Cup of tea? How do you like it?
Alice: Oh, yes thank you. Milk and no sugar. [Pauses] Excuse me, sir, but how did your hair get like that?
Had Matter: What's wrong with it?
Alice: I didn't say there was anything wrong with it. I was just wondering how it got like that.
Had Matter: Two sugars, was it?
Alice: No, no sugar, thank you. You are rather odd. What is it like being a mad hatter?
Had Matter: I'm not a mad hatter. Have you ever met a hatter? I'm Mr Matter. What's it like to matter, you ask? Would you like to try? I'd quite like to be an Alice.
Alice: How did you know my name was Alice?
Had Matter: No information escapes me! Here's your tea, with three sugars, as you like it.
Alice: Er, thank you very much. Yes, I'd like to try being a Mr Matter. Maybe we could exchange places?
Had Matter: Maybe we just did! Maybe I was Alice just a moment ago, only I don't remember being Alice, else I wouldn't be Mr Matter. I think I'm Mr Matter. Hmm.
Alice: Where's Bob? I need to send him a message.
Had Matter: I never invited Bob to my party. Come to think of it, I never invited you either. And you can't send a message, 'cause my butler's on a picnic.
Alice: Oh, I don't need a butler. It's all arranged...