Using Inverse lambda and Generalization to Translate English to Formal Languages

We present a system to translate natural language sentences to formulas in a formal or a knowledge representation language. Our system uses two inverse λ-calculus operators and using them can take as input the semantic representation of some words, phrases and sentences and from that derive the semantic representation of other words and phrases. Our inverse λ operator works on many formal languages including first order logic, database query languages and answer set programming. Our system uses a syntactic combinatorial categorial parser to parse natural language sentences and also to construct the semantic meaning of the sentences as directed by their parsing. The same parser is used for both. In addition to the inverse λ-calculus operators, our system uses a notion of generalization to learn semantic representation of words from the semantic representation of other words that are of the same category. Together with this, we use an existing statistical learning approach to assign weights to deal with multiple meanings of words. Our system produces improved results on standard corpora on natural language interfaces for robot command and control and database queries.