Thank you, Ben! The part I found most interesting was about type-raising being link-crossing. Type-raising seemed very mysterious, at first. And link-crossing in LG seemed impossible until the day I realized that non-planar electrical circuit diagrams are drawn on flat pieces of paper all the time.
There's a trick: an electric wire arrives, out of the blue, on one side, jumps over, and leaves into the yonder on the other side. Written with types, this has the distinctive signature W -> T- & W & T+ where the wire to be crossed is W, and the one doing the crossing is T. It's mysterious only in that one thinks "what the heck is T and where did it come from?" and the answer is "it doesn't matter, T came from somewhere out there, and then it left again, leaving us untouched, as we were before." Once you see this pattern, it is not hard to spot. It's also a great way to do long-range coordination in LG. It shows how something distant can affect local behavior: this distant thing just hops over whatever is in the way, until it arrives in the local area. -- Linas On Sat, Jul 16, 2022 at 11:42 AM Ben Goertzel <[email protected]> wrote: > Nice work Linas! Indeed this correspondence was always conceptually > clear, but it's good to see it worked out in detail for the first > time... > > On Sat, Jul 16, 2022 at 9:33 AM Linas Vepstas <[email protected]> > wrote: > > > > Alas, I attached a PDF that contains errors, instead of a URL to a PDF > where the latest and greatest version can be found. So -- a mistake is > fixed, and additional clarification is provided. The presentation is now > much stronger. Here: > > > https://github.com/opencog/atomspace/raw/master/opencog/sheaf/docs/ccg.pdf > > > > On Thu, Jul 14, 2022 at 1:13 PM Linas Vepstas <[email protected]> > wrote: > >> > >> The relationship between different grammar formalisms is almost always > cloudy and opaque. Sometimes, it's how the grammar is formalized, > sometimes, it's the notation. > >> > >> In the case of Combinatory Categorial Grammar, it's the notation. After > a minor, almost trivial restructuring of the notation, it can be seen to be > equivalent to Link Grammar. See attached PDF. > >> > >> Thanks to Adam Vandervorst, who raised this in an OpenCog Discord chat > discussion. I've long known of this equivalence, having sensed it by > gut-feel. However, having to actually write it out, in detail, to make it > convincing to others, was ... educational. > >> > >> -- Linas > >> > >> -- > >> Patrick: Are they laughing at us? > >> Sponge Bob: No, Patrick, they are laughing next to us. > >> > >> > > > > > > -- > > Patrick: Are they laughing at us? > > Sponge Bob: No, Patrick, they are laughing next to us. > > > > > > -- > > You received this message because you are subscribed to the Google > Groups "opencog" group. > > To unsubscribe from this group and stop receiving emails from it, send > an email to [email protected]. > > To view this discussion on the web visit > https://groups.google.com/d/msgid/opencog/CAHrUA36QWsN1j-apJsZL9w4EEqb5CZFLwoXbsW%3DAc11oO3pZ-w%40mail.gmail.com > . > > > > -- > Ben Goertzel, PhD > [email protected] > > "My humanity is a constant self-overcoming" -- Friedrich Nietzsche > > -- > You received this message because you are subscribed to the Google Groups > "opencog" group. > To unsubscribe from this group and stop receiving emails from it, send an > email to [email protected]. > To view this discussion on the web visit > https://groups.google.com/d/msgid/opencog/CACYTDBdw6dCcyVfZNLPX2M0cZQmfByS5Joh26G%2BP7X%3D8iNRaLQ%40mail.gmail.com > . > -- Patrick: Are they laughing at us? Sponge Bob: No, Patrick, they are laughing next to us. -- You received this message because you are subscribed to the Google Groups "opencog" group. To unsubscribe from this group and stop receiving emails from it, send an email to [email protected]. To view this discussion on the web visit https://groups.google.com/d/msgid/opencog/CAHrUA34LbYkrVNJZOC5dSSoASjHp%3DjpY0X8PS%3DWCLwBXdin8YA%40mail.gmail.com.
