SUO: Logic, Topic Maps, and RDF

["John F. Sowa" <sowa@bestweb.net>]

Murray, Peter, and Jack,

I'm breaking this thread in two because we have
got on a speparate track here with Topic Maps.

But before getting into more detail about these
questions, let me reiterate some points that I have
made time and again:

  1. Logic is fundamental to every issue and facet
     of knowledge representation and related subjects,
     such as topic maps, conceptual modeling, RDF,
     database design, ontology, etc., etc., etc.

  2. In the middle ages, logic, grammar, and rhetoric
     were the first three of the seven liberal arts.
     Every university student learned them at the very
     beginning of the curriculum.  Those topics remained
     in the curriculum until the late 19th century (and
     some "backwards" schools continuted to teach them
     even until the middle of the 20th century).

  3. Logic is no more difficult than 9th grade algebra,
     and it is an unfortunate mistake to let students
     graduate from high school, let alone college,
     without learning the basics of logic.

  4. Although our schools are woefully inadequate and
     became more so during the 20th century, it is no
     excuse for anyone who aspires to do serious work
     in the subjects mentioned in point #1 to allow his
     or her education to stagnate at the 8th grade level.

  5. Anybody who is working on the subjects listed in
     point #1 and does not know logic is as incompetent
     as a college graduate who can't read beyond the 8th
     grade level.

At the end of this note are some recommended readings for
anyone who aspires to rise out of a state of incompetence.

 From Murray's note:

 > Despite claims to the contrary, most of those I'm aware
 > of who've spent a lot of time looking at the two models
 > now say that the two systems' models [CGs and TMs] are
 > incompatible -- that you can write transforms between
 > their syntaxes (it's been done for several years), but
 > that the meaning of many types of statements are either
 > incorrect or impossible to state.

You've been talking to too many people who haven't done
their homework.  Please send them a copy of this note.
Following are the basic issues:

  1. Conceptual graphs are a formally defined system of
     logic with a direct mapping to and from predicate
     calculus and other systems of logic.

  2. Topic maps have been described in very informal ways
     without proper attention to their logical foundation.
     As Allan Perlis said, "You cannot translate an informal
     statement to a formal statement by any formal algorithm."
     Therefore, I certainly agree with your statement above.

  3. In so far as TMs can be formalized, what they represent
     are metalevel statements about the kinds of relationships
     that may hold between instances of certain types rather
     than the relationships that do hold between any instances.

  4. For example, the triple Husband->Married->Wife is a
     statement about how entites of type Husband are related
     to entities of type Wife.  In that sense, they are
     similar to the Entity-Relationship diagrams used
     in database design.

  5. Conceptual graphs can be used either at the object
     level or at the metalevel.  At the object level,
     the following CG can be translated to the sentence
     "Some husband is married to some wife.":

     [Husband]->(Married)->[Wife].

     I certainly agree that is not the intended
     interpretation of the triple shown above.

  6. However, CGs can also be used to represent any
     intended metalevel interpretation of a TM.
     The following CG, for example, states that
     the relation type named Married has one argument,
     which is of type Husband, and another argument,
     which is of type Wife:

     [RelationType: Married]-
         (HasArg)->[ConceptType: Husband]
         (HasArg)->[ConceptType: Wife].

  7. With appropriate axioms for stating how types
     are related to instances, the above CG could be
     used to derive the following object-level CG:

     [If:  [Person: *x]->(Married)->[Person: *y]
        [Then:
           [Or:
              [[Husband: *x] [Wife: *y]]
              [[Wife: *x] [Husband: *y]] ] ] ].

     This says that if person x is married to person y,
     then either x is a husband and y is a wife
          or x is a wife and y is a husband.

I admit that the mapping I have shown here is probably
not the "obvious" syntactic mapping that your friends
may have used.

 > Topic Maps are a specific paradigm. They're neither
 > a subset of RDF nor of CGs. I think it's a gross
 > simplification to conflate the three.

I would delete the word "paradigm", which Thomas Kuhn used
in a defensible way, but which has now degenerated to a
meaningless buzz word.

To be precise, I would make the following claims:

  1. When RDF is used precisely (which is rather rare for
     most people who use it), it expresses a subset of
     Common Logic.  (Pat Hayes is a consultant to the W3C,
     and he has worked to ensure that statement is correct.)

  2. Conceptual graphs and KIF express a much larger subset
     of Common Logic, which includes the semantics of RDF
     (as defined by Pat Hayes and the W3C) as a proper subset.

  3. Topic Maps can be mapped to RDF triples.  However, those
     triples usually represent metalevel relationships among
     types rather than object-level relationships among
     instances.  But if RDF is used as a metalevel language,
     then the metalevel subset expressed by RDF is a subset
     of the metalevel language expressed by CGs and KIF.

Following are some recommended readingst, which I strongly
urge anyone with an interest in topic maps to read and study.

John
____________________________________________________________

Before getting into the reading list, let me mention that
I do *not* recommend the highly technical versions of logic
that were invented by Boole, Frege, and Peirce as the best
introductions to logic.  I certainly recommend them to more
advanced students, but not to beginners.

For everybody (both those have studied logic in college and
those who haven't), I would recommend the following book,
which is essentially an updated version of the way logic,
grammar, and rhetoric were taught in medieval universities:

    Joseph, Sister Miriam (1937) _The Trivium: The Liberal Arts
    of Logic, Grammar, and Rhetoric, Third edition 1948,
    reprinted by Paul Dry Books, 2002.   Available in paperback
    for $11.87 (Amazon.com).

Following is a review from a reader on Amazon:

    This book is as much fun as I've had from a book in quite
    some time, even though the subject matters (grammar,
    logic, rhetoric) are usually thought of as serious if
    not outright grim.

    The book was originally written for first-year students
    at college in the 1930s and 40s. It is simply amazing
    how much knowledge the teacher could assume from her
    students and build on....

    After introductory chapters on the liberal arts and
    on language, two chapters on grammar (which are not
    dull summaries of long-familiar rules - in the 1930s
    these could be taken as given) lead smoothly into
    several chapters on logic, ending with a fine chapter
    summarizing fallacies. This material will be challenging,
    but a lot of fun, and for the most part presented with
    great clarity....

    Highly recommended - a 6-star book if ever there was one.

That book covers logic at the level of Aristotle's syllogisms,
but it does something that most so-called "modern" logic
courses do not emphasize:  the analysis of language and
concepts expressed in language and the mapping of language
to logic.  If anyone doing knowledge representation has
only time to read one book, I strongly recommend this one.

For a review of the "modern" notation for logic, you can
start with my 37-page overview (actual page count may
vary, depending on your font size):

    http://www.jfsowa.com/logic/math.htm
    Mathematical Background

Beyond that, the choice of books would depend very
strongly on the reader's background.  I would suggest
that people dust off any of their old college textbooks
that introduce logic and reread them (or at least skim
them).  Another possibility is to browse through the
books on logic at a good library and pick one or two
that seem interesting.

I would recommend my own textook on knowledge representation,

    Sowa, John F. (2000) _Knowledge Representation:  Logical,
    Philosophical, and Computational Foundations_, Brooks/Cole
    Publishing Co., Pacific Grove, CA.

but unfortunately, Amazon is selling it for the outrageous
price of $84.25.  The publisher originally told me that the
retail price would be about $40 -- but they lied.  If you
are at a university or a company with a library, I suggest
that you ask the librarian to buy it.

As an overview of the issues about metalevels and logic,
see the following paper on my web site:

    http://www.jfsowa.com/ontology/ontometa.htm
    Ontology, Metadata, and Semiotics

And for an introduction to logic by Peirce, you can read
my annotated version of his manuscript 514:

    http://www.jfsowa.com/peirce/ms514.htm
    Existential Graphs

All of this is just scratching the surface of what there
is to know, but for anybody who wants to do knowledge
representation in topic maps, RDF, or any other notation,
it is absolutely essential to know logic.  Start studying.