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Subject: Re: [xdi] Inference and equivalence defintion/notation (and $has)
Hello, sure, I agree that the +a/$has/+b statement "produces" the new composite subject +a+b (and viceversa); formally I think this can be expressed as +a/$has/+b <=> +a+b but, as Bill pointed out: saying "Bill's email" is somehow different that saying "Bill has an email". Therefore I think that they are not aliases: +a/$has/+b != +a+b Does it make sense? Kind Regards, Giovanni Def. Quota "Drummond Reed" <drummond.reed@xdi.org>: > Giovanni, > > I'm missing something. The whole premise of $has statements is that they > produce a new XDI subject which is the concatenation of the $has subject and > the $has object. > > So why do you say +a/$has/+b != +a+b ? > > =Drummond > > On Sun, Jan 17, 2010 at 1:52 PM, Giovanni Bartolomeo < > giovanni.bartolomeo@uniroma2.it> wrote: > >> Can we have && for AND maybe (C, C++, Java et al.)? >> >> >> You asked about the following >>>> >>>> :+a/$has/+b = (+a/+b) = +a+b >>>> >>>> Yes, I think so. Though this presents a hefty practicality concern that >>>> =Bill+email now resolves to the graph of statements about the statement >>>> (=Bill/+email), rather than a set of statements describing Bill's email. >>>> >>> >> I also fear they represent different concepts. >> >> +a/$has/+b = (+a/+b) maybe, but >> >> >> +a/$has/+b != +a+b >> >> Kind Regards, >> Giovanni >> >> Def. Quota "Drummond Reed" <drummond.reed@xdi.org>: >> >> >> Bill, >>> >>> Just a quick note to say that of course I agree let's use the terms that >>> are >>> widely established in the semantic community. I only typed /= last night >>> because I was too tired to remember the notation (I really shouldn't stay >>> up >>> that late) and I wanted to follow up on yesterday's conversation quickly. >>> >>> I like all of your notation and suggest we adopt it. Doe everyone else >>> agree? (Let me put it this way - anyone who does not agree, please post, >>> otherwise let's use Bill's notation.) >>> >>> I don't have time right at this moment to answer the questions at the >>> bottom >>> of your message, but I'll try to get back to it later today, as I think >>> we've got the foundation now to complete a semantically deeper and >>> stronger >>> definition of $has and $has$a, and with my improved understanding of the >>> notation, we might even be able to make good progress on that in email. >>> >>> Thanks, >>> >>> =Drummond >>> >>> On Fri, Jan 15, 2010 at 5:51 AM, Barnhill, William [USA] < >>> barnhill_william@bah.com> wrote: >>> >>> Hi Drummond, >>>> >>>> Your email makes sense but I have a few things I'd like to ehar what you >>>> think about: >>>> >>>> The terms I was using 'logical equivalence', 'implies/implication', '!= >>>> for >>>> not equal' are not terms I created. They're terms in wide adoption within >>>> semantic community and in the case of !=, the development community. >>>> Typically what you're calling inference is isually termed implication. I >>>> haven't encountered the terms you used before, so what do you think about >>>> using the following terms and notation instead: >>>> >>>> >>>> Implication => (there's no >>>> need for <= as A <= B is stated as B => A) >>>> >>>> Logical equivalence <=> >>>> >>>> Alias (ie resolution equivalence) == >>>> >>>> Non-equivalence != >>>> >>>> And ^ >>>> >>>> Or || >>>> >>>> Not And (NAND) | >>>> >>>> Exclusive Or (XOR) ~| >>>> >>>> Nor (Not Or) !| >>>> >>>> >>>> >>>> The notation for the boolean operations NAND, XOR, and NOR >>>> above >>>> are my own. The std notation is >>>> >>>> not easily entered into plain text except as an image. >>>> >>>> >>>> >>>> You asked about the following >>>> >>>> :+a/$has/+b = (+a/+b) = +a+b >>>> >>>> Yes, I think so. Though this presents a hefty practicality concern that >>>> =Bill+email now resolves to the graph of statements about the statement >>>> (=Bill/+email), rather than a set of statements describing Bill's email. >>>> >>>> >>>> >>>> :+a/$has/+b /= +a/+b >>>> >>>> Yes the right one contains statements about the value of the left one, >>>> the >>>> left statements about the value of the +b property of +a. >>>> >>>> >>>> >>>> :+a/+b /= +a+b >>>> >>>> Yes the left one contains statements about the value of the +b property >>>> of >>>> +a, the right statements about the left one. >>>> >>>> >>>> >>>> :+a/$has$a/+b = +a/+b >>>> >>>> Don't know. I never got the feeling we nailed down $has$a enough for me >>>> to >>>> make this determination. I still do not like $a as an inverse operator, >>>> would prefer defining inverse $ words for the key concepts like $has, >>>> maybe >>>> $hadby. I think we have to nail $has down real well before we can define >>>> the >>>> inverse of it. >>>> >>>> >>>> >>>> :+a/$has$a/+b /= (+a/+b) >>>> >>>> See above. >>>> >>>> >>>> Kind regards, >>>> >>>> Bill Barnhill >>>> Booz Allen Hamilton - Rome, NY >>>> 315-330-7386 | william.barnhill.ctr@rl.af.mil | >>>> barnhill_william@bah.com >>>> >>>> ------------------------------ >>>> *From:* drummond.reed@gmail.com [drummond.reed@gmail.com] On Behalf Of >>>> Drummond Reed [drummond.reed@xdi.org] >>>> *Sent:* Friday, January 15, 2010 5:12 AM >>>> *To:* OASIS - XDI TC >>>> *Subject:* [xdi] Inference and equivalence defintion/notation (and $has) >>>> >>>> Bill, >>>> >>>> >>>> >>>> In thinking about your definitions of "logical equivalence" and >>>> "resolution >>>> equivalence" today, I'm wondering if we couldn't just use the terms >>>> "inference" and "equivalence". In other words, it is easier for me to >>>> understand the differences between the sentence "XDI statement A infers >>>> XDI >>>> statement B" and the sentence "XDI statement A is equivalent to XDI >>>> statement B". >>>> >>>> >>>> >>>> My understanding of inference is that it can be unidirectional (A infers >>>> B >>>> but B does not infer A) or bi-directional (A infers B and B infers A). >>>> >>>> >>>> >>>> My understanding of equivalence is that it must be bidirectional, i.e., >>>> if >>>> A is equivalent to B then B MUST be equivalent to A. This is the purpose >>>> of >>>> XDI $is statements – they express equivalence between an XDI subject and >>>> and >>>> XDI object. >>>> >>>> >>>> >>>> If you agree these terms will work, let's use your proposed notation: >>>> >>>> >>>> >>>> Unidirectional inference <= or => >>>> >>>> Bidirectional inference <=> >>>> >>>> Equivalence = >>>> >>>> Non-equivalence /= >>>> >>>> >>>> >>>> With that said I can restate the first part of the final conclusion of >>>> today's telecon (see >>>> http://lists.oasis-open.org/archives/xdi/201001/msg00046.html for the >>>> chat >>>> transcript) as saying that: >>>> >>>> >>>> >>>> +a/$has/+b <=> (+a/+b) <=> +a/+b <=> +a+b >>>> >>>> >>>> >>>> This is true because each infers the other, and all these inferences are >>>> bidirectional (I think). >>>> >>>> >>>> >>>> This would also imply that: >>>> >>>> >>>> >>>> +a <=> (+a) >>>> >>>> >>>> >>>> Again, this is because each implies the other (I have one small >>>> reservation >>>> about this but I'll save that for another time). >>>> >>>> >>>> >>>> And part two of our final conclusion of the telecon was that: >>>> >>>> >>>> >>>> +a /= (+a) >>>> >>>> >>>> >>>> This is true because as you described resolving (doing a $get) on +a and >>>> (+a) respectively would not return the same graph. >>>> >>>> >>>> >>>> Lastly, we can finally get to the definition of $has and $has$a >>>> statements. >>>> What I have been saying (but not expressing with the proper notation) is: >>>> >>>> >>>> >>>> +a/$has/+b = (+a/+b) = +a+b >>>> >>>> >>>> >>>> +a/$has/+b /= +a/+b >>>> >>>> >>>> >>>> +a/+b /= +a+b >>>> >>>> >>>> >>>> +a/$has$a/+b = +a/+b >>>> >>>> >>>> >>>> +a/$has$a/+b /= (+a/+b) >>>> >>>> >>>> >>>> Do you agree? >>>> >>>> >>>> >>>> =Drummond >>>> >>>> >>>> >>>> >>>> >>>> >>>> >>>> >>>> >>>> >>> >> >> >> ---------------------------------------------------------------- >> This message was sent using IMP, the Internet Messaging Program. >> >> >> --------------------------------------------------------------------- >> To unsubscribe from this mail list, you must leave the OASIS TC that >> generates this mail. Follow this link to all your TCs in OASIS at: >> https://www.oasis-open.org/apps/org/workgroup/portal/my_workgroups.php >> > ---------------------------------------------------------------- This message was sent using IMP, the Internet Messaging Program.
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