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In this paper we share several experiments trying to automatically translate informal mathematics into formal mathematics. In our context informal mathematics refers to human-written mathematical sentences in the LaTeX format; and formal…
We study methods for automated parsing of informal mathematical expressions into formal ones, a main prerequisite for deep computer understanding of informal mathematical texts. We propose a context-based parsing approach that combines…
Informal mathematical text underpins real-world quantitative reasoning and communication. Developing sophisticated methods of retrieval and abstraction from this dual modality is crucial in the pursuit of the vision of automating discovery…
In order to work with mathematical content in computer systems, it is necessary to represent it in formal languages. Ideally, these are supported by tools that verify the correctness of the content, allow computing with it, and produce…
We report on our experiments to train deep neural networks that automatically translate informalized LaTeX-written Mizar texts into the formal Mizar language. To the best of our knowledge, this is the first time when neural networks have…
In machine translation field, in both academia and industry, there is a growing interest in increasingly powerful systems, using corpora of several hundred million to several billion examples. These systems represent the state-of-the-art.…
Autoformalization has emerged as a term referring to the automation of formalization - specifically, the formalization of mathematics using interactive theorem provers (proof assistants). Its rapid development has been driven by progress in…
Generating natural language requires conveying content in an appropriate style. We explore two related tasks on generating text of varying formality: monolingual formality transfer and formality-sensitive machine translation. We propose to…
This paper proposes a natural language translation method for machine-verifiable formal proofs that leverages the informalization (verbalization of formal language proof steps) and summarization capabilities of LLMs. For evaluation, it was…
Autoformalization is the task of translating natural language materials into machine-verifiable formalisations. Progress in autoformalization research is hindered by the lack of a sizeable dataset consisting of informal-formal pairs…
In this chapter we provide an overview of computational modeling for semantic change using large and semi-large textual corpora. We aim to provide a key for the interpretation of relevant methods and evaluation techniques, and also provide…
Before we can get the whole potential of employing computers in the process of managing mathematical `knowledge', we have to convert informal knowledge into machine-oriented representations. How exactly to support this process so that it…
A biform theory is a combination of an axiomatic theory and an algorithmic theory that supports the integration of reasoning and computation. These are ideal for specifying and reasoning about algorithms that manipulate mathematical…
A probabilistic model for computer-based generation of a machine translation system on the basis of English-Russian parallel text corpora is suggested. The model is trained using parallel text corpora with pre-aligned source and target…
While neural machine translation (NMT) has become the new paradigm, the parameter optimization requires large-scale parallel data which is scarce in many domains and language pairs. In this paper, we address a new translation scenario in…
While the progress of machine translation of written text has come far in the past several years thanks to the increasing availability of parallel corpora and corpora-based training technologies, automatic translation of spoken text and…
The goal of universal machine translation is to learn to translate between any pair of languages, given a corpus of paired translated documents for \emph{a small subset} of all pairs of languages. Despite impressive empirical results and an…
Model transformation tools assist system designers by reducing the labor--intensive task of creating and updating models of various aspects of systems, ensuring that modeling assumptions remain consistent across every model of a system, and…
The ability to compare the semantic similarity between text corpora is important in a variety of natural language processing applications. However, standard methods for evaluating these metrics have yet to be established. We propose a set…
Formality plays a significant role in language communication, especially in low-resource languages such as Hindi, Japanese and Korean. These languages utilise formal and informal expressions to convey messages based on social contexts and…