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Perhaps stupid question but I ask nonetheless.

The question: Can Formal languages have a concept of a verb? If never, why can't they?

Context: In natural language, we have verbs to describe action. In Formal language (eg: Natural deduction), I only see statements. I have never seen something concepts like "subject" , "verb" or "object" in N.D. However, clearly Formal Language still has a Grammar. There is still a syntax to say what makes sense and what doesn't.

This leads me to the impression that requirement to go from Natural to Formal is to give up verbs.

Related questions:

Explaining Formal language trough a Natural one

Is Art beyond logic?

tryst with freedom
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    There's nothing fundamentally non-formal about verbs. Look at dynamic logics or TLA, for example. – Noah Schweber Oct 09 '22 at 21:22
  • "is" is a verb. https://writingexplained.org/is-is-a-verb – user4894 Oct 09 '22 at 21:24
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    Is there much difference between verbs and the usual predicates in formal languages?... – Double Knot Oct 10 '22 at 02:09
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    Some have theorized that in programming (a kind of formal language), functions can be seen as verbs (and variables as nouns). – armand Oct 10 '22 at 04:28
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    in line with @NoahSchweber's comment, consider a simple imperative language, with commands such as "skip", "loop", "assign". more generally, it depends on what you mean by verb. In any case tho, verbs or lack thereof aren't the best characterization for the distinction between formal and natural languages – emesupap Oct 10 '22 at 14:49
  • @TrystwithFreedom The only fundamental difference is that natural languages are natural, in the sense that no one designed them, they just arise out of the interactions between people, while formal languages are invariably created and developed purposefully. To answer your question, formal languages are created for some specific purpose so that whether there are verbs only depends on the needs of the creators of the language. Programming languages are perhaps the epitome of formal languages and they have verbs, verbs which express the actions the programmer wants the computer to perform. – Speakpigeon Oct 10 '22 at 16:12
  • Yes. The goal of all languages (formal or informal) is to communicate. How would you replace the verb "to be" in "a triangle IS a polygon"? The equal sign is essentially a verb "to be", in pi=3.1416 (which reads "pi is three..."). How would you skip it? – RodolfoAP Feb 17 '23 at 13:21

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