Hi Linas, The difference between PartitionLink and MemberLink is pretty obvious, right? A PartitionNode defines a partition of the set denoted by a ConceptNode. The partition elements that are linked to the PartitionNode by a PartitionLink can of course also be linked via a MemberLink to the ConceptNode that corresponds to the PartitionNode. However, the unique semantics of a partition is that of mutual exclusivity and completeness, i.e. the intersection between two distinct elements of the partition is null, and the union of the elements of the partition is the set being partitioned. This semantics is implicit in PartitionNode, whereas if you just use MemberLink you'd need to spell out this "partition" semantics using a bunch of AndLinks each time...
As a world-class advocate of the partition function I think you may like PartitionNode after you reflect on it infinitesimally more... -- ben On Tue, Aug 1, 2017 at 5:54 AM, Linas Vepstas <[email protected]> wrote: > Hi Ben, Mike, > > On Fri, Jul 21, 2017 at 9:41 PM, Ben Goertzel <[email protected]> wrote: >> >> Some interesting representational issues have come up in the context >> of Atomspace representation of pathways, which appear to have more >> general implications… >> >> It seems the semantics we want for a biological pathway is sort of >> like “the pathway P is a set of relationships R1, R2, …, R20” in kinda >> the same sense that “the human body is a set of organs: brain, heart, >> lungs, legs, etc.” >> >> First of all it seems what we have here is a part of relationship… maybe >> we want >> >> PartLink >> ConceptNode “heart” >> ConceptNode “human-body” >> >> and >> >> PartLink >> >relationship< >> >pathway< >> >> PartLink and PartOfLink have come and gone in >> OpenCog/Novamente/Webmind history... >> >> An argument that PartLink should have fundamental status and a >> well-defined fuzzy truth value is given in this paper: >> >> https://www.academia.edu/1016959/Fuzzy_mereology >> >> However what we need for biological pathways and human bodies seems >> like a bit more. We want to say that a human body consists of a >> certain set of parts... not just that each of them is a part... We're >> doing a decomposition. >> >> One way to do this would be >> >> PartitionLink >> ConceptNode “human-body” >> ListLink >> ConceptNode “legs” >> ConceptNode “arms” >> ConceptNode “brain” >> etc. >> >> Relatedly, we could also have > > > As mentioned earlier, there are several problems with this format. One is > the "oops I forgot to mention xyz in the list" or "gosh I should have left > out pqr" and this becomes a big problem: you have to delete the > PartitionLink, delete the ListLink, create a new list and partition. In the > meanwhile, some other subsystem might be holding a handle to the old, > now-wrong PartitionLink, and there is no effective way of announcing "hey > stop using that old thing, get my new thing now". > > A second problem is that the above doesn't have anywhere to hang addtional > data: e.g. "legs are a big part of the human body, having a mas of nearly > half of the body." You can't just slap that on as a (truth)value, cause > there's no where to put that value. > > Third problem is that large list-links are hard to handle in the pattern > matcher. Its much much harder to write a query of the form "find me all > values of $X where > > PartitionLink > ConceptNode “human-body” > ListLink > ConceptNode “legs” > VariableNode “$X” > ConceptNode “brain” > > because, ... well the ListLink is an ordrerd link, not an unordered link. If > you forget to include the pqr (added above) then the search will fail. You > could try to use unordered links and globnodes, but these lead to other > difficulties, including the n! possible permutations of an unordered link > become large n-factorial large when the unordered link has n items in it. > Recall that old factorial-70 trick used to make calculators overflow. > > In general, any link with more than 3 or 4 or 5 items in it is bad news. > This is a generic statement about knowledge representation in opencog. > > >> OverlappingPartitionLink >> C >> L >> >> if we want to encompass cases where the partition elements in L can >> overlap; or >> >> CoveringLink >> C >> L >> >> if we want to encompass cases where the partition elements in L can >> overlap, AND the elements in L may encompass some stuff that’s not in >> C >> >> For the pathway case, we could then say >> >> PartitionLink >> ConceptNode “Krebs cycle” >> ListLink >> >relationship 1< >> >relationship 2< >> etc. >> >> >> Now this solves the semantics problem but doesn’t solve the problem of >> having a long ListLink…. A biological pathway might have 100s or >> 1000s of relationships in it, and we don't usually want to make lists >> that big in the Atomspace... >> >> To solve this we could do something like (for the human body case) >> >> PartitionLink >> ConceptNode “human-body” >> PartitionNode “body-partition-1” >> >> PartitionElementLink >> PartitionNode “body-partition-1" >> ConceptNode “legs” >> >> PartitionElementLink >> PartitionNode “body-partition-1" >> ConceptNode “arms” >> >> etc. >> >> and similarly (for the biological pathway case) >> >> PartitionLink >> ConceptNode “Krebs cycle” >> PartitionNode “krebs-partition-1” >> >> PartitionElementLink >> PartitionNode “krebs-partition-1" >> >relationship 1< >> >> PartitionElementLink >> PartitionNode “krebs-partition-1” >> >relationship 2< > > > > Yeah, sure. Not sure why the existing MemberLink is not sufficient for your > purposes. The MemberLink has reasonably-well-defined semantics, there are > already rules for handling it in PLN (or there will be rules -- I think its > something Nil has thought about) I'm not clear on why you'd want to invent > something that is just like MemberLink but is different. > >> >> >> ... >> >> There could be some nice truth value math regarding these, e.g. we >> could introduce Ellerman's "logical entropy" which is really a >> partition entropy. There are also connections with some recent >> theoretical work I've been doing on "graphtropy" (using "distinction >> graphs" that generalize partitions), which I'll post a paper on >> sometime in the next week or two.... But that will be another email >> for another day... > > > Yeah graphical-entropy is something that I keep trying to work on, except > that every new urgent disaster of the day distracts me from it. > > --linas >> >> >> -- Ben >> > -- > 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 post to this group, send email to [email protected]. > Visit this group at https://groups.google.com/group/opencog. > To view this discussion on the web visit > https://groups.google.com/d/msgid/opencog/CAHrUA35kQx%3DyDcLTynrThvi%3DrAVa15D-1PSwZpK_37Q%3DjZhcfw%40mail.gmail.com. > For more options, visit https://groups.google.com/d/optout. -- Ben Goertzel, PhD http://goertzel.org "I am God! I am nothing, I'm play, I am freedom, I am life. I am the boundary, I am the peak." -- Alexander Scriabin -- 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 post to this group, send email to [email protected]. Visit this group at https://groups.google.com/group/opencog. To view this discussion on the web visit https://groups.google.com/d/msgid/opencog/CACYTDBdm6M1y18G%3DQi%3D_rjJcdrEb5eAmx8ntxffKoRw_dG1OYw%40mail.gmail.com. For more options, visit https://groups.google.com/d/optout.
