Diagrams Series 3 Notation

The diagram notation acts as a kind of syntax, except that the smallest element which participates in the syntax is an entire phrase or sentence rather than a word or part of a word. Complex configurations are built up from simple ones by a mechanism similar to that by which in ordinary syntax complex sentences are built up from simple sentences by transforming the simple sentences into clauses and phrases.
 
 

1. Basic Configurations

The simplest configurations involve connecting two or three phrases by lines which terminate with a #. The type of configuration depends on the symbols that occur along the line. Where a line takes a jog by means of the symbol: 
\ /
 |
or any of its spatial rotations: 
            /     \
   |      --       --
  / \,      \,    /
this indicates that the configuration contains a verb. The verb is the element found by following in the direction of the vertex of the V-shape. The configuration: 
                                               a
                                               |
                                               #
a -#----\ /----#- b                            |
         |                                     |
         |                                     /
         #                 or      c -#--------
         |                                     \
         c                                     |
                                               |
                                               #
                                               |
                                               b
is like a simple sentence in which c acts as the verb. The roles of a and b are symmetrical, however, unlike the subject and object of an ordinary sentence. There may also be two-element configurations which contain a verb. 
a -#----\ /       or           \
         |                      --------#- b
         |                     /
         #                     |
         |                     |
         b                     #
                               |
                               a
is like a simple sentence of the form "subject - predicate", with b playing the role of the predicate. There are two kinds of basic configuration in which there is no verb. The configuration: 
                                a
a -#----+--                     |
        +-----#-b      or       #
                                |
                                |
                                +-+
                                | |
                                  |
                                  |
                                  #
                                  |
                                  b
is like a phrase of the form "a modified by b". In this case a is dominant over b. Note that the dominant element can be distinguished from the modifier no matter what the spatial orientation, since the line to the dominant element goes straight, and the line to the modifier branches out from the line to the dominant element. The configuration: 
a -#--------#-b       or       a
                               |
                               #
                               |
                               |
                               |
                               |
                               #
                               |
                               b
has no direct analogue in ordinary grammar. It is a phrase in which a and b are directly juxtaposed, but the relationship is symmetrical and without further structure.

2. Complex Configurations

Complex configurations involve the same kinds of connecting lines as above, but the elements at the ends of the lines may be other configurations, rather than phrases. Where a configuration is enclosed in a loop of dots, e.g. 
 . . . . . . . . . . . .
.                       .
.  a -#----\ /----#- b  .
 .          |          .
  .         |         .
   .        #        .
    .       |       +-#----\ /
     .      c      .        |
      .           .         |
       . . . . . .          #
                            |
                            d
the configuration enclosed in the dots acts like a phrase or clause. In this case the configuration containing a, b, and c is acting like a noun clause in the configuration in which d occurs as the verb. In addition to a phrase or a loop of dots, the end-point of a connecting line may also be another connecting line. The rough meaning of this is that the element in the configuration is the action of the connecting line. In the configuration: 
a -#---\ /
        |
        |
        +-#----\ /----#- c
        |       |
        #       |
        |       #
        b       |
                d
the third element in the basic configuration involving c and d is the action of the verb b on a.

3. Parenthesis and Arrow

In some cases a connecting line which is part of a basic configuration may not end with the symbol #, but will end with parentheses. The parentheses denote that there is an open place for the entry that would normally be at the end of the connecting line. The parentheses are like the variable X in algebra. X holds a place for any number which may then be substituted into a given spot in a formula; the parentheses likewise hold open a place in a structural configuration that would normally be occupied by an entry.

When the symbol # is attached to an arrow which terminates between parentheses, the # denotes the filling of the position held open by the parentheses.

4. Parsing

Parsing should begin with the basic configurations whose entries are all phrases. If there are loops of dots inside other loops, parsing should begin inside the innermost loop. The configuration below has numbers next to each basic configuration to indicate an order in which the basic configurations may be read for the easiest parsing. Other orderings may be equivalent. 
  . . . . . . . . . . . . . . . . . . . . .
 .                                         .
.          2         . . . . . . . . . . .  .
.  a -#----+--      .          1          .  .
 .         +-----#-+  b -#----\ /----#- c  .  .
  .                .           |           .  .           3
   .                .          |          .  .           \ /----#- e
    .                .         |         .  .             |
     .                .        #        .  .      5       |
      .                .       |       .  +-#----\ /----#-+
       .                .      d      .  .        |       |
        .                .           .  .         |       |
         .                . . . . . .  .          |       #
          .                           .           |       |
           . . . . . . . . . . . . . .            |       f
                                                  |
                                                  |
                                                  #
                                                  |
                                          g -#----+----#- h
                                                  4


Diagrams Series 3