CAN NEURAL NETWORKS UNDERSTAND LOGICAL ENTAILMENT?
We introduce a new dataset of logical entailments for the purpose of measuring models' ability to capture and exploit the structure of logical expressions against an entailment prediction task. We use this task to compare a series of architectures which are ubiquitous in the sequence-processing literature, in addition to a new model class-PossibleWorldNets-which computes entailment as a "convolution over possible worlds". Results show that convolutional networks present the wrong inductive bias for this class of problems relative to LSTM RNNs, treestructured neural networks outperform LSTM RNNs due to their enhanced ability to exploit the syntax of logic, and PossibleWorldNets outperform all benchmarks.
SUMMARY 
The paper is fairly broad in what it is trying to achieve, but the approach is well thought out. The purpose of the paper is to investigate the effectiveness of prior machine learning methods with predicting logical entailment and then provide a new model designed for the task. Explicitly, the paper asks the following questions: "Can neural networks understand logical formula well enough to detect entailment?", and "Which architectures are best at inferring, encoding, and relating features in a purely structural sequence-based problem?". The goals of the paper is to understand the learning bias of current architectures when they are tasked with learning logical entailment. The proposed network architecture, PossibleWorldNet, is then viewed as an improvement on an earlier architecture TreeNet.
POSITIVES 
The structure of this paper was very well done. The paper attempts to do a lot, and succeeds on most fronts. The generated dataset used for testing logical entailment is given a constructive description which allows for future replication. The baseline benchmark networks are covered in depth and the reader is provided with a deep understanding on the limitations of some networks with regard to exploiting structure in data. The PossibleWorldNets is also given good coverage, and the equations provided show the means by which it operates.
• A clear methodological approach to the research. The paper covers how they created a dataset which can be used for logical entailment learning, and then explains clearly all the previous network models which will be used in testing as well as their proposed model.
• The background information regarding each model was exceptionally thorough. The paper went into great depth describing the pros and cons of earlier network models and why they may struggle with recognizing logical entailment.
• The section describing the creation of a dataset captures the basis for the research, learning logical entailment. They describe the creation of the data, as well as the means by which they increase the difficulty for learning.
• The paper provides an in depth description of their PossibleWorldNet model, and during experimentation we see clear evidence of the models capabilities.
NEGATIVES
One issue I had with the paper is regarding the creation of the logical entailment dataset. Not so much for how they explained the process of creating the dataset, that was very thorough, but the fact that this dataset was the only means to test the previous network models and their new proposed network model. I wonder if it would be better to find non-generated datasets which may contain data that have entailment relationships. It is questionable if their hand crafted network model is learned best on their hand crafted dataset.
The use of a singular dataset for learning logical entailment. The dataset was also created by the researchers for the express purpose of testing neural network capacity to learn logical entailment. I am hesitant to say their proposed network is an incredible achievement since PossibleWorldNet effectively beat out other methods on a dataset that they created expressly for it.
RELATED WORK 
The paper has an extensive section dedicated to covering related work. I would say the research involved was very thorough and the researchers understood how their method was different as well as how it was improving on earlier approaches.
CONCLUSION 
Given the thorough investigation into previous networks’ capabilities in logical entailment learning, I would accept this paper as a valid scientific contribution. The paper performs a thorough analysis on the limitations that previous networks face with regard to exploiting structure from data. The paper also covers results of the experiments by not only pointing out their proposed network’s success, but by analyzing why certain earlier network models were able to achieve competitive learning results. The structure of the PossibleWorldNet was also explained well, and during ex- perimentation demonstrated its ability to learn structure from data. The paper would have been improved through testing of multiple datasets, and not just on there self generated dataset, but the contribution of their research on their network and older networks is still justification enough for this paper.