General Discussion

I think there are two problems that make this hard to answer:

1. Not all sentences that can be parsed grammatically can also be parsed logically.

2. Human-language sentences do not contain all the information needed to evaluate them.

It is impossible to fully separate context from human language in general. The sentence "it is cold" is perfectly valid, and logically coherent, but in order to evaluate it you'd need to draw external information from the context. What is "it"? Maybe we can assume "it" refers to the weather, as that is common usage, but that information does not come from the sentence itself. And since the context here is on the Internet, where there is no understanding of location, we can't really evaluate it that way.

It's hot somewhere, and it's cold somewhere. Does that mean the statement "it is cold" is both true and false, or does that mean there is insufficient information to evaluate it in the first place? I think this is largely a matter of convention. I have no doubt that you could construct a coherent system that would classify such statements as being in a superposition of truth and falsehood. Whether that would be useful is another matter. You might also need a probabilistic model instead of a simple three-state evaluation of true/false/both. I mean, if we're talking about human language, we're talking about things that are at least a little subjective.

So I don't think the question can be evaluated properly without defining a more restrictive category of "sentences". It seems to me like the question uses "sentence" to mean "logical statements", but without a clearer definition I don't know how to approach that. Sentences are not the same as logical statements. If they were, we wouldn't need programming languages :)

Apologies for the half-baked ideas. I think it would take a lifetime to fully bake this.