Logic in sentence : tree representation
Syntaxnet parser could surely help you in parsing the sentences and in tree represenation.

If you plan on solving using RNNs, I believe Tree LSTM will be a better choice than LSTM, as it also preserves dependency information. 
Full paper.

Use Tree LSTM, if you need a vector embedding for the whole sentence. For use cases like classification, sentiment analysis. It works and there is a good probability that the vector could have all the information but you may not be certain and thats why its still a black box. But, if your use case is a clear representation of tree structure and logic among the terms (which you wanted), better go with parsers like Syntaxnet and try rule-based models for the use case mentioned.