Bootstrapping Lexical Choice via Multiple-Sequence Alignment

An important component of any generation system is the mapping dictionary, a lexicon of elementary semantic expressions and corresponding natural language realizations. Typically, labor-intensive knowledge-based methods are used to construct the dictionary. We instead propose to acquire it automatically via a novel multiple-pass algorithm employing multiple-sequence alignment, a technique commonly used in bioinformatics. Crucially, our method leverages latent information contained in multi-parallel corpora -- datasets that supply several verbalizations of the corresponding semantics rather than just one. We used our techniques to generate natural language versions of computer-generated mathematical proofs, with good results on both a per-component and overall-output basis. For example, in evaluations involving a dozen human judges, our system produced output whose readability and faithfulness to the semantic input rivaled that of a traditional generation system.Comment: 8 pages; to appear in the proceedings of EMNLP-200

The use of data-mining for the automatic formation of tactics

This paper discusses the usse of data-mining for the automatic formation of tactics. It was presented at the Workshop on Computer-Supported Mathematical Theory Development held at IJCAR in 2004. The aim of this project is to evaluate the applicability of data-mining techniques to the automatic formation of tactics from large corpuses of proofs. We data-mine information from large proof corpuses to find commonly occurring patterns. These patterns are then evolved into tactics using genetic programming techniques

Learning Mathematics as a Language

This paper explores the relationship between language and mathematics. It is a summary of research done over the last thirty years. Also included are personal observations which are not part of any controlled study. Since language is the vehicle for thought, mathematics educators and curriculum planners will benefit from a linguistic approach to mathematics education. Symbolic mathematics is similar to natural language in both its structure and its communicative nature. If the students are to internalize the notation, they must be the ones to give it meaning. A linguistic approach to mathematics education includes language development, verbalization of concepts, vocabulary development, and written work. The child learns language through a sequence of listening, speaking, reading, and writing. This sequence is inherent in problem solving. The true purpose of mathematics education is to equip the student with the ability to understand a problem, formulate a plan to solve it, carry out that plan, and be able to tell if the answer they get is reasonable. An approach to mathematics instruction that addresses the language of mathematics will help provide the student with this ability

Three Approaches to Generating Texts in Different Styles

Natural Language Generation (nlg) systems generate texts in English and other human languages from non-linguistic input data. Usually there are a large number of possible texts that can communicate the input data, and nlg systems must choose one of these. We argue that style can be used by nlg systems to choose between possible texts, and explore how this can be done by (1) explicit stylistic parameters, (2) imitating a genre style, and (3) imitating an individual’s style

An Interactive Viewer for Mathematical Content Based On Type Theory

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