[om-list] Re: Cyc example

[Tom and other Packers]

Mark

    I've never heard anyone call them "qualifiers" but me, either.  The reason I do this is the following.  In mathesis, every complete idea has both a quantity and a quality (an arbitrarily-defined state).  One is meaningless without the other.  This is one of the central, key points in MME (The MetaMathesis Essay).  Quality is meaningless without quantity, and vice versa.  If you don't agree, ... well, we've had this conversation before, and my egoistically-optimistically-warped memory tells me that I won that argument -- but I could be wrong.  

    Anyway, since quantity is taken care of by the quantifier in each of these expressions:
    "x or $x

quality is everything else, i.e. the variable, "x".  The variable represents some state, a quality.  
 
    This obviously applies only to variables in predicate or propositional calculus (and "logic of noun expressions", as Britannica calls it), not in mathematics.  In mathematics, variables mainly represent quantities -- and perhaps qualities too, depending on how you look at them.  The quality aspect is completely (infinitely) generalised to represent any quality, unless units are given, in which case, units restrict (specify or qualify) the quality.  

    Actually, vector variables have both quality and quantity.  Magnitude is quantity, direction is quality.  



    I agree with Mark on names.  One thought I have: names and naming is just one more relation or attribute to be added to any given node/entity.  All relations/attributes should be taken into consideration if/when models (worldviews) are merged.  For example, if two nodes are candidates for merger, and each has an attribute which are mutually exclusive, then these two nodes cannot be merged into identical nodes.  (I.e. their relation is not the "identity relation", which is a vector of length zero; rather their relation is some other vector of a finite, and probably small, length).  
 
    For example, when merging two theism models together, if one model says that a "god" is mortal (e.g. Norse mythology, where gods can and do die) and the other says that a "god" is immortal, (e.g. Mormonism), then we can't combine both "gods", because we are not really talking about exactly the same thing.  They have a shorter relational vector than most nodes in the model will have, but it is not the zero (identity) vector.  

    Therefore, (I just wanted to make sure we're all on the same page), identical names is not a sufficient criterion for making the associated nodes identical.  
 
    Furthermore, it's also not a necessary criterion.  Two nodes having the same name can be a sufficient reason to *consider* combining them, but not necessary (e.g. synonyms, which must be compared using the other relations and attributes).  



    About language/notation: I've recently been working on a idea modelling notation along the lines of predicate calculus predicates.  It's based on a very simple system (but can be extended as needed) in which all operations and propositions are represented as a three-token list, (recursively if necessary).  This is a very simple and straight-forward system that I'd like you guys to consider once I'm done with it.  
 
    It's fairly flexible.  We can leave it up to the user to decide which order these tokens come in.  For example, he might prefer the standard format of predicate calculus, mathematics, and Prolog, like Mark seems to:

    P(O1 O2) or P(O1,O2)

Or he might prefer the more enlightened format of LISP :-) 

    (P O1 O2)

Or he might prefer this relation-enhancing format:

    (O1 P O2)

 All of these forms are easily accommodated.  Here "P" represents the predicate, relation, operator, function-name, internode, intranode, etc; and the two "O"s represent operands, nodes, arguments, parameters, etc.  There is a clear distinction between internodes and intranodes in mathesis (i.e. there is a clear distinction between functions and relations -- one is static, the other dynamic), but there is also a clear and necessary and significant similarity between them, too.  The MME is basically a list of pairs of concepts, where each member of these pairs is inseparably dependent on the other member of the pair, like quantity and quality, symbolics and geometrics, etc.  Another of the main principles (points) in the MME is the dependency of the dynamic and static portions of a model.  The bottom line here is, operations are based on relations.  Therefore, I believe that the notation of functions should be based very closely on the notation for relations.  I think this will be beneficial to the human reader as well as to the search algorithms that process queries and other things, just like the pattern-matchers (like the "unification algorithm", which I think is a silly name) in rule-based expert systems and such.  

    Conjecture: all knowledge can be represented as a list of expressions, each of which is a combination of (possibly nested) three-token lists.  
 
    We wouldn't want to represent all knowledge this way, but I think it should be based on this simple form.  And I think operators and functions should be a very slight variation of the static relation notation, e.g. 

    (P O1 [O2]) or (P O1 O2) or (P O1 [ ]) 

    (I hope you guys have HTML-email readers.)  Here, the return value is one of the nodes in the list with special indication, like brackets or underlining.  For some functions, the function name would be the token specified as the return value.  It all depends on what function you want.  The significant thing to catch here is, all relations have exactly three corresponding functions associated with them, and therefore each return value can be indicated based on the basic, static, binary-relational notation.  I'll explain how all this works later, if anyone is interested.  But it sufficeth me to say that I strongly believe that all knowledge, including all existing functions or operators in math, logic, etc., can be represented as a binary operator plus its two operands.  

    Upon this, we can define conventions for lists of more or less than three atoms/tokens/variables to make it more flexible, and more "LISPy".  

Luke, 

    yes, we can certainly find someplace to discuss this stuff when you come.  Jeremy and/or Doug has a whiteboard.  Or we could go to Thoughtform in Bountiful, which has many.  

Mark

    I think I'm leaning toward the meta-meta-model idea, but I don't think I understand the question well enough to answer definitively yet.  Let's talk about this.

ciao,
tomp


----- Original Message ----- 
From: Mark Butler <butlerm at middle.net>
To: Thomas L. Packer <TomP at burgoyne.com>
Cc: <om-list at onemodel.org>
Sent: Thursday, September 28, 2000 11:06 PM
Subject: Re: [om-list] Re: Cyc example


"Thomas L. Packer" wrote:

>     Mark, in Predicate Calculus (including first order predicate calculus),
> they are called "quantifiers", including the existential quantifier and
> universal quantifier.  

Yes. My mistake.

> The variables they quantify are the qualities. 

I have never heard variables called qualities and cannot imagine why one would
call them that.  Do you have an explanation and some references?

- Mark

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