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    • CommentRowNumber1.
    • CommentAuthorWillemMali
    • CommentTimeAug 4th 2017
    I'm sorry for barging in on your forum as a relative newbie to mathematics. I'm looking for learning resources, I put a tl;dr at the bottom.

    I'm a programmer by trade and have recently acquired the urge to build a solid formal foundation for structuring the data I collect, which includes news articles, books, scientific papers, research datasets and much more. To get closer to this goal I am going to develop a semantic database with the purpose of representing any and all human knowledge formally. (Good starter project, no?)

    I've come to the conclusion that if I am to structure the very wide range of knowledge I want to represent, I will not only have to use mature NLP techniques (for acquiring the set of all possible interpretations) in combination with either human aid or statistical/ML techniques for disambiguation, I will then have to find a mathematical foundation that is able to represent all of mathematics, because I anticipate needing a lot of mathematics to get at all close to being able to represent all human knowledge formally and also because I think having most if not all the mechanics behind the system be represented inside the system will be the only way to make it flexible enough to get close to representing all human knowledge including all knowledge from all sciences.

    Once I have a working system I will then extend it to have isolation as a data management and security feature, add more ways of interfacing with the database (e.g. via streams) and then implement federation through implementing models of trust and related algorithms in the system and connecting that to a distributed data index such as the output of a BitTorrent DHT crawler. The end result I envision is a crossing between a knowledge base, a computation engine and a wiki, which can be used as any and all of those.

    Some elements I think I will need to be able to represent at the very least are:

    - numbers, bytes, words, mathematical formulas, theorems, tables, images, files...
    - relations between any possible object in the database (e.g. between sets, functions and relations between higher level relations)

    It would be ideal I could start with a relatively simple model on which to build the more complex model that is capable of encompassing much more if not all of mathematics.

    Some of the possible applications of this semantic database would be:

    - (initially heavily human-aided) conversion of novel mathematical objects to a formal representation that is also executable (e.g. import new pages on nLab and hand-annotate them -> directly use the new concepts in computations)
    - analysis of news on a wide range of aspects (e.g. representations of different groups, logical consistency, consistency with source material, consistency and conflicts with related articles, consistency with related scientific literature)
    - automatic inference (e.g. new weather data comes in, combine with existing corpus on weather and seismic data -> new model of predicted weather, combine with models on how weather affects human beings -> storm warning)
    - formalize scientific papers to find out if they are internally inconsistent or otherwise faulty, and also analyze them for external consistency (in relation to other papers) and on their effects of the probabilities of propositions they have in common with other research papers, this could potentially be very useful pre-publication but also dangerous because it opens the door for manipulation
    - expert systems
    - accidentally creating AGI
    - extracting parts of the knowledge base to get consistent formal models for many knowledge domains

    I'm a bit afraid that the response will be "congratulations, you've basically invented Lisp and this is why it won't work" because I haven't learned Lisp yet and because I have some vague sense that there is similarity between this idea and the ideas behind Lisp. If so, please pick apart my post in the greatest possible detail, I would absolutely love that because I'm very isolated from the mathematics community and I could use any and all feedback.

    I have some familiarity with algebra, formal logic, set theory and NLP, but it's quite limited. Reading the nLab right now is very intimidating, although I think I might've found a small foothold from directed graph -> quiver -> category.

    tl;dr: I'm looking for recommendations reading material on how to build a knowledge base capable of representing all of mathematics, remarks on why this is a bad idea or who tried before me are also very appreciated, and I'd also appreciate a "required reading list" for nLab.
    • CommentRowNumber2.
    • CommentAuthorspitters
    • CommentTimeAug 4th 2017
    • (edited Aug 4th 2017)

    Quick answer. Are you aware of the field of mathematical knowledge managemant?

    • CommentRowNumber3.
    • CommentAuthorWillemMali
    • CommentTimeAug 4th 2017
    I wasn't, thank you! The nearest discipline I'd found so far was ontology-based knowledge management/engineering, but this gets me a lot closer.