I am trying to represent the following statement, which contains "unless", into propositional logic:
If it's snowing when I am outdoors I get cold unless I am wearing a coat.
Using the following propositions:
Snowing, Outdoor, Cold, WearingCoat
Here's my attempt however I am not sure if it's the right representation:
$$(Snowing \land WearingCoat \land Outdoor) \to -Cold $$
I'm not sure what proportional logic is (it sounds neat!), but as Brian suggests in the comments, the standard logical interpretation of "unless" is if not. Under this interpretation, "I get cold unless I am wearing a coat" means I get cold if I am not wearing a coat, and can be represented formally as $$\lnot\text{WearingCoat}\rightarrow\text{Cold}$$ To motivate this interpretation of "unless", consider a statement like "We won't make the train unless you hurry." When I say this, I'm saying that if you don't hurry, we're not going to make the train. I'm not saying that if you do hurry, we're going to make the train.
With that said, the entire statement "If it's snowing when I am outdoors, [then] I get cold unless I am wearing a coat" could be represented as $$(\text{Snowing}\land\text{Outdoor})\rightarrow(\lnot\text{WearingCoat}\rightarrow\text{Cold})$$ or equivalently $$(\text{Snowing}\land\text{Outdoor}\land\lnot\text{WearingCoat})\rightarrow\text{Cold}$$