Changes

==Graphical calculi==

==Graphical calculi==

{{main|Logical graph}}

 

: ''Main article'' : [[Logical graph]]

It is possible to generalize the definition of a formal language from a set of finite sequences over a finite basis to include many other sets of mathematical structures, so long as they are built up by finitary means from finite materials.  What's more, many of these families of formal structures are especially well-suited for use in logic.

It is possible to generalize the definition of a formal language from a set of finite sequences over a finite basis to include many other sets of mathematical structures, so long as they are built up by finitary means from finite materials.  What's more, many of these families of formal structures are especially well-suited for use in logic.

For example, there are many families of [[graph (mathematics)|graph]]s that are close enough analogues of formal languages that the concept of a calculus is quite easily and naturally extended to them.  Indeed, many species of graphs arise as ''[[parse graph]]s'' in the syntactic analysis of the corresponding families of text stuctures.  The exigencies of practical computation on formal languages frequently demand that text strings be converted into [[pointer structure]] renditions of parse graphs, simply as a matter of checking whether strings are wffs or not.  Once this is done, there are many advantages to be gained from developing the graphical analogue of the calculus on strings.  The mapping from strings to parse graphs is called ''[[parsing]]'' and the inverse mapping from parse graphs to strings is achieved by an operation that is called ''[[graph traversal|traversing]]'' the graph.

For example, there are many families of graphs that are close enough analogues of formal languages that the concept of a calculus is quite easily and naturally extended to them.  Indeed, many species of graphs arise as ''parse graphs'' in the syntactic analysis of the corresponding families of text structures.  The exigencies of practical computation on formal languages frequently demand that text strings be converted into pointer structure renditions of parse graphs, simply as a matter of checking whether strings are wffs or not.  Once this is done, there are many advantages to be gained from developing the graphical analogue of the calculus on strings.  The mapping from strings to parse graphs is called ''parsing'' and the inverse mapping from parse graphs to strings is achieved by an operation that is called ''traversing'' the graph.

==Other logical calculi==

==Other logical calculi==