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The idea I'm thinking of is about a top-down approach for AI. I would like to know if there can be a model for computers so that they can perform causal reasoning. It seems that causal relation can be simplified to be a mathematical structure, as an acyclic directed graph. If using type theory, one builds some "time types" $\{\sigma_i,i\in\mathbb{N}\}$ ($\mathbb{N}$ as an index set denoting time points). The variable inhabit different time types means they are at different time points. The signature can be constructed according to the existing causal relation. The formation rule is such constructed that the rules for formulas with variables from the same time types are the same as usual logic, and the rules for different time types are based on the causal relation.

Can someone comment about this idea and give some general review about the development of top-down approach, also about causal reasoning?

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    $\begingroup$ What is it precisely that you hope to achieve with this approach? 'AI' is a very vague term, but I guess you're mainly interested in some sort of knowledge representation and automated reasoning? What sort of reasoning precisely? Furthermore, could you explain what this has to do with LTL? $\endgroup$
    – Discrete lizard ♦
    Feb 10, 2018 at 22:16
  • $\begingroup$ @Discretelizard Yes I’m interested in that, some kind of dynamic reasoning. But I’m not sure how to represent the dynamic process. A maths theory won’t change across time but one’s knowledge is changing, like a time-dependent logic. So I think of using different types for different time. I suppose it might have something to do with temporal logic, not sure though. I ever had a look at temporal logic. It bears a bit similar ideas, though looks like linguistic. I think it’s because a more explicit description for causal relation needs more than just simplifying it as a directed graph. $\endgroup$
    – user84187
    Feb 10, 2018 at 22:49
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    $\begingroup$ I'm not sure what you mean. We don't know any physical process that a Turing machine can't simulate, so why do you need a new model of computation? Either the thing you want to do can already be done by the existing models of computation, or it probably can't be done by any physically realizable computer. $\endgroup$
    – David Richerby
    Feb 11, 2018 at 13:08
  • $\begingroup$ @DavidRicherby Is that AI can't think in a more human-like way, not because the model for computers is not good enough, but the process of complicated thinking can't be realised? Is that the reason why people use neuron networks for AI to achieve some complicated task instead of building an overall algorithm for the task? $\endgroup$
    – user84187
    Feb 11, 2018 at 14:12
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    $\begingroup$ @Nicky As far as we know, the existing model for computers can do everything that is physically possible in the universe. Sure, it's possible that there are as-yet-unknown physical processes that can't be modelled by Turing machines but, unless we discover one of those, what does it mean to say that Turing machines aren't "good enough"? "Artificial Intelligence" is just a collection of algorithms with a catchy name: it's not capable of doing stuff that algorithms can't do because it is algorithms. $\endgroup$
    – David Richerby
    Feb 11, 2018 at 14:19

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This is a hot topic at the moment. Read this recent paper by Judea Pearl for example. In general, ML and AI are not very good at causal inference at the moment, because it requires a symbolic representation to build causal graphs. Attempts are being made, however, see e.g. https://arxiv.org/abs/1711.08936 or https://arxiv.org/abs/1709.05321.

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