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Atrium > Mathematics, Physics & Philosophy: Entropy in logic,logic and probability

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    • CommentRowNumber1.
    • CommentAuthorBeNikis
    • CommentTimeOct 29th 2013
    • (edited Oct 31st 2013)
    Recently I've been thinking about the syntax-semantics adjunction.Now,to be clear,I've read a lot of category theory and find it intuitively beautiful,but still can't grasp the specifics of what the definition of an adjunction 'means',so bear with me.
    Ok-since there is an adjunction between the theories of a logic and the models of those theories,maybe there is a need to somehow meld probability theory and logic using category theory/categorical logic?Since machine learning as far as I read of artificial intelligence is much easier in probability theory,and also it would be much easier to generate random numbers based on the learned distribution,probabilities would give the creativity part of true intelligence,and logic would be used to structure what the AI agent learned.

    As I see it,the end goal of this idea is an algorithm based on the syntax-semantics adjuntion that would learn (semantics->;syntax) and then generate (syntax->semantics) hypotheses about the subject,then test it out and learn based on reinforcement methods.Basically the end goal would be a general algorithm for the scientific method,which sounds crazy,but i've been thinking about this for a few years and just need to let this out in the open,since I don't yet have the appropriate knowledge or skills to work this idea out whether it's semi-feasible or not.

    Also,if I'm thinking staright,then maybe we could use the curry-howard isomorphism and metaprogramming to write an AI agent that would improve itself,but this is bordering on sci-fi and this is why I'm writing this-to know wether or not I'm yet another crackpot.
    • CommentRowNumber2.
    • CommentAuthorTobyBartels
    • CommentTimeOct 29th 2013

    If you suspect that you might be a crackpot, then you almost surely are not! I don't think that your goals here are inherently crazy, but I also don't have a clear enough grasp of your proposal to know whether it is crazy.

    • CommentRowNumber3.
    • CommentAuthorTobyBartels
    • CommentTimeOct 29th 2013

    (Looks like I loaded this page between three and six hours ago!)

    • CommentRowNumber4.
    • CommentAuthorBeNikis
    • CommentTimeOct 29th 2013
    Sorry - I got embarrased and edited my post out :)

    My basic idea is this:combine probabilities and logic using category theory,use that in artificial intelligence.

    Sorry if I don't use big words like left adjoint or kan extension or whatever-I'm only a second year student who shopuld've graduated this summer with a BS in computer science,but life got in the way.I'm afraid that by using those terms in the wrong way i'd look like a fool.
    • CommentRowNumber5.
    • CommentAuthorTobyBartels
    • CommentTimeOct 29th 2013

    Just stick a question mark in parentheses right after each word that you may have used incorrectly. That's what I do. (^_^)

    • CommentRowNumber6.
    • CommentAuthorTim_Porter
    • CommentTimeOct 29th 2013

    Have you looked at some of the posts on the n-Cat café which discussed combining probability and category theory (skimming them is all that is needed)? Your idea of using such a mix in artifical intelligence is a good one. I looked at something a bit on those lines some years back, but other projects got prioritised.

    • CommentRowNumber7.
    • CommentAuthorBeNikis
    • CommentTimeOct 30th 2013
    Hey Thanks!There's a lot to digest there but i'll go through it.
    • CommentRowNumber8.
    • CommentAuthorBeNikis
    • CommentTimeOct 30th 2013
    • (edited Oct 30th 2013)
    Also - the book "Thinking fast and slow" Daniel Kahneman seems to suggested that the way people process information is too divided into two parts - the intuitive one which as I see it resembles the probabilistic side , and the more formal one,which would be logic.Just started reading that book though,but dual process theory seems very similar to this.

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