Changes

In lieu of better names, and in hope of a better reason to come in good time, we may for the moment refer to these two forms of transformation as ''[[axiom]]s'' or ''initials''.

In lieu of better names, and in hope of a better reason to come in good time, we may for the moment refer to these two forms of transformation as ''[[axiom]]s'' or ''initials''.

==Duality, logical and topological==

==Duality : logical and topological==

There are two types of [[duality (mathematics)|duality]] that have to be kept separately mind in the use of logical graphs, [[De Morgan's laws|logical duality]] and [[topology|topological]] [[dual graph|duality]].

There are two types of [[duality (mathematics)|duality]] that have to be kept separately mind in the use of logical graphs, [[De Morgan's laws|logical duality]] and [[topology|topological]] [[dual graph|duality]].

In the case of our last example, a moment's contemplation of the following picture will lead us to see that we can get the corresponding parenthesis string by starting at the root of the tree, climbing up the left side of the tree until we reach the top, then climbing back down the right side of the tree until we return to the root, all the while reading off the symbols, in this particular case either "(" or ")", that we happen to encounter in our travels.

In the case of our last example, a moment's contemplation of the following picture will lead us to see that we can get the corresponding parenthesis string by starting at the root of the tree, climbing up the left side of the tree until we reach the top, then climbing back down the right side of the tree until we return to the root, all the while reading off the symbols, in this particular case either "(" or ")", that we happen to encounter in our travels.

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<p>[[Image:Logical_Graph_Figure_6.jpg|center]]</p>

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This ritual is called ''[[tree traversal|traversing]]'' the tree, and the string read off is often called the ''[[traversal string]]'' of the tree.  The reverse ritual, that passes from the string to the tree, is called ''[[parsing]]'' the string, and the tree constructed is often called the ''[[parse tree|parse graph]]'' of the string.  The speakers thereof tend to be a bit loose in this language, often using ''[[parse string]]'' to mean the string that gets parsed into the associated graph.

This ritual is called ''[[tree traversal|traversing]]'' the tree, and the string read off is often called the ''[[traversal string]]'' of the tree.  The reverse ritual, that passes from the string to the tree, is called ''[[parsing]]'' the string, and the tree constructed is often called the ''[[parse tree|parse graph]]'' of the string.  The speakers thereof tend to be a bit loose in this language, often using ''[[parse string]]'' to mean the string that gets parsed into the associated graph.