>>16683319
a modality in general is just a way to qualify the truth of a proposition. Examples are:

necessity:
>[math]P[/math] is possibly true (typically rendered as [math]\Box P [/math])
>[math]P[/math] is necessarily true (typically rendered as [math]\diamond P[/math])
>[math]P[/math] is known to be true

Traditional logic only allows you to evaluate expressions as "true" or "false" but not the qualifications used above. Modal logics add modal operators and semantics that allow you to express and perform inference on expressions like [eqn]\Diamond P \rightarrow \Box Q[/eqn] I.e.: (If P is possibly true, then Q must be necessarily true).

It had its use in AI in the sense that was used in symbolic AI approaches that were most relevant around the 80s and 00s. The approach of symbolic AI is to encode as much domain knowledge in formal logic and allow logical program solvers to draw conclusions. That being said, this form of AI stands orthogonal to the current statistics based approaches of AI that you are probably thinking of when you talk about AI. ChatGPT does not explicitly encode modal logic for instance.

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What exactly is modal logic