Typed Answer Set Programming and Inverse Lambda Algorithms

Our broader goal is to automatically translate English sentences into formulas in appropriate knowledge representation languages as a step towards understanding and thus answering questions with respect to English text. Our focus in this paper is on the language of Answer Set Programming (ASP). Our approach to translate sentences to ASP rules is inspired by Montague's use of lambda calculus formulas as meaning of words and phrases. With ASP as the target language the meaning of words and phrases are ASP-lambda formulas. In an earlier work we illustrated our approach by manually developing a dictionary of words and their ASP-lambda formulas. However such an approach is not scalable. In this paper our focus is on two algorithms that allow one to construct ASP-lambda formulas in an inverse manner. In particular the two algorithms take as input two lambda-calculus expressions G and H and compute a lambda-calculus expression F such that F with input as G, denoted by F@G, is equal to H; and similarly G@F = H. We present correctness and complexity results about these algorithms. To do that we develop the notion of typed ASP-lambda calculus theories and their orders and use it in developing the completeness results. (To appear in Theory and Practice of Logic Programming.)

Solving puzzles described in English by automated translation to answer set programming and learning how to do that translation

We present a system capable of automatically solving combinatorial logic puzzles given in (simplified) English. It involves translating the English descriptions of the puzzles into answer set programming(ASP) and using ASP solvers to provide solutions of the puzzles. To translate the descriptions, we use a lambda-calculus based approach using Probabilistic Combinatorial Categorial Grammars (PCCG) where the meanings of words are associated with parameters to be able to distinguish between multiple meanings of the same word. Meaning of many words and the parameters are learned. The puzzles are represented in ASP using an ontology which is applicable to a large set of logic puzzles.

Language understanding as a step towards human level intelligence - automatizing the construction of the initial dictionary from example sentences

For a system to understand natural language, it needs to be able to take natural language text and answer questions given in natural language with respect to that text; it also needs to be able to follow instructions given in natural language. To achieve this, a system must be able to process natural language and be able to capture the knowledge within that text. Thus it needs to be able to translate natural language text into a formal language. We discuss our approach to do this, where the translation is achieved by composing the meaning of words in a sentence. Our initial approach uses an inverse lambda method that we developed (and other methods) to learn meaning of words from meaning of sentences and an initial lexicon. We then present an improved method where the initial lexicon is also learned by analyzing the training sentence and meaning pairs. We evaluate our methods and compare them with other existing methods on a corpora of database querying and robot command and control.

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 lambda-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 lambda 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 lambda-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.