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discarded1023 • today at 12:54 AM • 1 reply • view on HN

This was a big concern when I was an undergrad in the 1990s. I've since wondered if bunched implications / separation logic / separation algebras / ... [1] that emerged in the early 2000s has resolved this well enough. Opinions?

At least some of the problem was due to people unnecessarily restricting themselves to first-order logic for knowledge representation, as advocated by John McCarthy [2].

[1] https://en.wikipedia.org/wiki/Separation_logic

[2] see e.g. https://www-formal.stanford.edu/jmc/concepts.pdf

Replies

Joker_vD • today at 1:17 AM

Heh. Reminds me of one of Lewis Carroll's sylogisms:

    Premise A: "No one, who means to go by the train and cannot get a conveyance, and has not enough time to walk to the station, can do without running";

    Premise B: "This party of tourists mean to go by the train and cannot get a conveyance, but they have plenty of time to walk to the station".

    Does the conclusion "This party of tourists need not run" hold?
It actually doesn't; here's a non-formulaic reason:

[Here is another opportunity, gentle Reader, for playing a trick on your innocent friend. Put the proposed Syllogism before him, and ask him what he thinks of the Conclusion.

He will reply “Why, it’s perfectly correct, of course! And if your precious Logic-book tells you it isn’t, don’t believe it! You don’t mean to tell me those tourists need to run? If I were one of them, and knew the Premisses to be true, I should be quite clear that I needn’t run—and I should walk!”

And you will reply “But suppose there was a mad bull behind you?”

And then your innocent friend will say “Hum! Ha! I must think that over a bit!”

You may then explain to him, as a convenient test of the soundness of a Syllogism, that, if circumstances can be invented which, without interfering with the truth of the Premisses, would make the Conclusion false, the Syllogism must be unsound.]