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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 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.
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.
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.
A distinguished symbol that is the start symbol, also called the sentence symbol. A grammar is formally defined as the tuple ( N , Σ , P , S ) {\displaystyle (N,\Sigma ,P,S)} . Such a formal grammar is often called a rewriting system or a phrase structure grammar in the literature.