For the required paper, the problem is to map the natural language sentences to logical forms, namely lambda calculus. The method proposed uses Combinatorial Categorical Grammar to induce the final logical forms, by summing out the possible ambiguous trees induced by the different initial lexical items aligned to the sentence. The main contribution of the paper, I feel, is the splitting categories method that induces the lexicon without manual engineered rules. Also the lexicon items can be multi-word expression, compared to prior work such as "Learning to Map Sentences to Logical Form: Structured Classification with Probabilistic Categorial Grammars" where the lexical items are usually single word predicate. The question I have is about the type function of lambda calculus, eg. I don't understand what logical form would be mapped to the form < e, < e,t > >, < e, t > does not seem to be a truth value.
For the additional paper, I read the paper:
Luke S. Zettlemoyer, Michael Collins. Learning Context-dependent Mappings from Sentences to Logical Form. In Proceedings of the Joint Conference of the Association for Computational Linguistics and International Joint Conference on Natural Language Processing (ACL-IJCNLP), 2009.
The idea is to map context dependent sentences to logical forms. The method proposed starts with a incomplete logical form for the target sentence as the first step, and this incomplete logical form is further combined with previous logical forms to obtain the final logical form as the second step. For the second step, the author proposes a model with a solution space of derivations, which are different configurations for deriving a final logical form. The inference is done through searching the best derivation in beam search based on the score of the derivation. The learning is done through Collins' perceptron which tunes the weight vectors corresponding to the feature vector of the derivation. I feel the most interesting idea is that they use the derivations as the output, and search for the best derivation, which would in turn generate the final logical form.