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In mathematical logic, a sentence (or closed formula) [1] of a predicate logic is a Boolean-valued well-formed formula with no free variables. A sentence can be viewed as expressing a proposition , something that must be true or false.
The consequence of these features is that a mathematical text is generally not understandable without some prerequisite knowledge. For example, the sentence "a free module is a module that has a basis" is perfectly correct, although it appears only as a grammatically correct nonsense, when one does not know the definitions of basis, module, and free module.
A logic translation is a translation of a text into a logical system.For example, translating the sentence "all skyscrapers are tall" as (() ()) is a logic translation that expresses an English language sentence in the logical system known as first-order logic.
In LaTeX text mode the math method above is inappropriate, as letters will be in math italic, so the command n\textsuperscript{th} will give n th and A\textsubscript{base} will give A base (textual subscripts are rare, so \textsubscript is not built-in, but requires the fixltx2e package). As in other systems, when using UTF-8 encoding, the ...
The language of mathematics has a wide vocabulary of specialist and technical terms. It also has a certain amount of jargon: commonly used phrases which are part of the culture of mathematics, rather than of the subject.
An open-source, math-aware, question answering system called MathQA, based on Ask Platypus and Wikidata, was published in 2018. [15] MathQA takes an English or Hindi natural language question as input and returns a mathematical formula retrieved from Wikidata as a succinct answer, translated into a computable form that allows the user to insert ...
a translator - used to translate a source language word into the target language; a TL morphological generator - works as a generator of appropriate target language words for the given grammatica information; a TL parser - works as a composer of suitable target language sentences; Several dictionaries - more specifically a minimum of three ...
Instead of fine-tuning a pre-trained language model on the translation task, sufficiently large generative models can also be directly prompted to translate a sentence into the desired language. This approach was first comprehensively tested and evaluated for GPT 3.5 in 2023 by Hendy et al.