When you ask, “What does it do?” what is “it” referring to? Modal logic? Counterfactuals? Stuart’s specific application of modal logic and counterfactuals?
Counterfactuals have found special application in causal inference. Lewis’ approach to counterfactuals provides a semantics for the Neyman-Rubin approach to causal inference. (See, for more detail, Glymour’s discussion piece following Holland’s well-known 1986 paper on causal inference.) Pearl takes it a step further by proving that the do() calculus is equivalent to Rubin’s and to Lewis’ approaches.
Your last question is a whole lot harder to answer. Maybe all of these things can be implemented in some way that does not require any modal logic or anything formally equivalent to modal logic. One might try a non-counterfactual approach to causal inference, like that suggested by Dawid, for example. (However, Dawid’s approach is not equivalent to the Neyman-Rubin-Lewis-Pearl approach: they don’t always endorse the same inferences.) I don’t know enough about AI approaches to the other problems to say whether or not modal logics have serious competitors. Maybe you could point me to some further reading(s)?
When you ask, “What does it do?” what is “it” referring to? Modal logic? Counterfactuals? Stuart’s specific application of modal logic and counterfactuals?
I’ll guess that you mean to ask about the whole apparatus of modal logic. Aside from Stuart’s stated goals—having to do with relevance and reactions to explosion and certain paradoxes, like the liar—modal logics have been used to study provability, knowledge and belief, moral obligation, tense, and action, just to name a few. You might also take a look at Section 3 of Benthem’s book Modal Logic for Open Minds for some applications of modal logic.
Counterfactuals have found special application in causal inference. Lewis’ approach to counterfactuals provides a semantics for the Neyman-Rubin approach to causal inference. (See, for more detail, Glymour’s discussion piece following Holland’s well-known 1986 paper on causal inference.) Pearl takes it a step further by proving that the do() calculus is equivalent to Rubin’s and to Lewis’ approaches.
Your last question is a whole lot harder to answer. Maybe all of these things can be implemented in some way that does not require any modal logic or anything formally equivalent to modal logic. One might try a non-counterfactual approach to causal inference, like that suggested by Dawid, for example. (However, Dawid’s approach is not equivalent to the Neyman-Rubin-Lewis-Pearl approach: they don’t always endorse the same inferences.) I don’t know enough about AI approaches to the other problems to say whether or not modal logics have serious competitors. Maybe you could point me to some further reading(s)?