|  An abstract example to illustrate a proposal for a Semantic Distance measure between terms in different namespaces.
|
|  Two players, A and B.  Their namespaces are only shared at the top of their taxonomies.
|
|   A Semantic Distance of 0 indicates that two terms can be used interchangeably.
|
|   A Semantic Distance of d>0 indicates that d name translations must be ruled out to get interchangeability.
|
|                  shared
|                  namespace
|                     AB0------A1--------A2_1
|                      `        `                  namespace A
|                       `        `-------A2_2
|                        `
|                         `----B1--------B2_1      namespace B
|
|
|   This agent illustrates how the formula below assigns a Semantic Distance of 1 between A2_1 and B2_1
|
|    SemanticDistance( x,n1,z,n2 ) =
|                min m [ exists( y) such that  shared( n1,n2,y ) &
|                             g( n1,x,y ) & g( n2,z,y ) &
|                             ( ( |{x1 : g( n1,x1,y ) }| + |{z1 : g( n2,z1,y ) }| ) = m ) ]  -  2
|                if such an m exists, else undefined



this-player uses the name this-name in namespace this-ns
========================================================
 A                         AB0                    S
 B                         AB0                    S


this-name1 is a this-name2 in namespace this-ns
===============================================
 A1               AB0                     A
 B1               AB0                     B
 A2_1             A1                      A
 A2_2             A1                      A
 B2_1             B1                      B


some-player1 uses the name some-name in namespace S
some-player2 uses the name that-name in namespace S
that-player1 and that-player2 are different
----------------------------------------------------------------------
that-player1 and that-player2 have agreed on the meaning of that-name


some-name1 is a bottom item in namespace some-ns1
some-name2 is a bottom item in namespace some-ns2
that-name1 and that-name2 are different
that-ns1 and that-ns2 are different
that-name1 is a some-name3 in namespace that-ns1
that-name2 is a that-name3 in namespace that-ns2
the-player1 and the-player2 have agreed on the meaning of that-name3
that-name3 specializes to some-number1 different bottom names in namespace that-ns1
that-name3 specializes to some-number2 different bottom names in namespace that-ns2
---------------------------------------------------------------------------------------------------
that-name1 in namespace that-ns1 that-number1 :: that-number2 matches that-name2 in namespace that-ns2


some-name1 in namespace some-ns1 some-number1 :: some-number2 matches some-name2 in namespace some-ns2
that-number1 + that-number2 = some-sum
that-sum - 2 = some-number
------------------------------------------------------------------------------------------------------------
that-name1 in namespace that-ns1 matches that-name2 in namespace that-ns2 with semantic distance that-number


some-name1 is a bottom item in namespace some-ns1
some-name2 is a bottom item in namespace some-ns2
that-name1 and that-name2 are different
that-ns1 and that-ns2 are different
that-name1 is a some-name3 in namespace that-ns1
that-name2 is a that-name3 in namespace that-ns2
the-player1 and the-player2 have agreed on the meaning of that-name3
-------------------------------------------------------------------------------------------
that-name1 in namespace that-ns1 and that-name2 in namespace that-ns2 resolve to that-name3


some-name1 is a bottom item in namespace some-ns
that-name1 is a some-name2 in namespace that-ns
-----------------------------------------------------------------------------------------------
the name that-name2 is a generalization of the bottom item name that-name1 in namespace that-ns


some-name2 occurs in namespace some-ns
count some-name1 : the name that-name2 is a generalization of the bottom item name that-name1 in namespace that-ns = a-number
-----------------------------------------------------------------------------------------------------------------------------
that-name2 specializes to that-number different bottom names in namespace that-ns


some-name1 is a some-name2 in namespace some-ns
that-name2 is a some-name3 in namespace that-ns
-----------------------------------------------
that-name1 is a that-name3 in namespace that-ns


some-name occurs in namespace some-ns1
that-name occurs in namespace some-ns2
that-ns1 and that-ns2 are different
--------------------------------------------------------------------
that-name is in the shared region of the namespaces that-ns1 that-ns2


some-ns1 is less than some-ns2
-----------------------------------
that-ns1 and that-ns2 are different


some-name1 is a some-name2 in namespace some-ns
-----------------------------------------------
that-name1 occurs in namespace that-ns


some-name1 is a some-name2 in namespace some-ns
-----------------------------------------------
that-name2 occurs in namespace that-ns


some-name2 occurs in namespace some-ns
some-name1 is a that-name2 in namespace that-ns
------------------------------------------------------
that-name2 has at least one child in namespace that-ns


some-name1 occurs in namespace some-ns
not : that-name1 has at least one child in namespace that-ns
------------------------------------------------------------
that-name1 is a bottom item in namespace that-ns