Are there any projects that can measure the concept similarity between texts? Are there any algorithms or software libraries that can be used to detect the similarity of concepts in text, regardless of articulation, grammar, synonyms, etc.?
For example, these phrases:

Outside, it is warm.
Outside, it is hot.
Outside, it is not cold.
It is not cold outside.

Should be similar to this phrase:

It is warm outside.

Ideally, the algorithm or software would be capable of generating a score from 0 to 1, based on the concept similarity. The goal is to use this algorithm or software to map a large number of statements to a single, similar original statement. It is for this mapping of a given statement to the original statement that the aforementioned similarity score would be generated.
Does such an algorithm of software already exist?
Doc2Vec

Doc2Vec comes to mind, here's the original publication. The approach has been shown to be very successful for certain NLP-based problems, though I haven't personally used it for a project yet. 

There are a number of implementations of Doc2Vec. If you're using Python, one to look at is gensim. 

Word2Vec

Word2Vec is similar to Doc2Vec and perhaps more in line with what you're looking for. Here's the original publication, and another publication that does a nice job explaining it further. 

Tensorflow has a tutorial for setting up a Word2Vec model. Gensim also has a Word2Vec implementation.