Defined Relation Type

 

goingTo

Here is an example in CG and IFF of a defined relation type that was taken from the CGIF standard. We paraphrase the standard. The conceptual graph for the sentence

“John is going to Boston by bus.”

can be represented as a binary expression by replacing the name John and the name Boston. The relation type goingTo can be defined by a conceptual graph that makes goingTo a synonym for a binary expression.

CG

The following gives a definition for the relation type goingTo. Two versions are given.

The first version in CG linear form uses an explicit binary definition relation with a relation type as its first argument and a lambda expression (of the same signature) as its second argument.

[Relation: goingTo] ® (Def) ® [LambdaExpression:

     [Person: l1] ¬ (agent) ¬ [Go] ® (destination) ® [City: l2]

]

The CGIF notation for the first version avoids the character l and represents lambda expressions in a form that shows the signature explicitly.

[Relation: goingTo] ® (Def) ® [LambdaExpression:

     (lambda

       (Person*x, City*y)

       [Go *z] (agent ?z ?x) (destination ?z ?y)

     )

]

The second version in CGIF uses the keyword relation, and a variable for each argument, as in the following definition of goingTo.

relation goingTo(*x *y) is

     [Person: ?x] ¬ (agent) ¬ [Go] ® (destination) ® [City: ?y]

IFF

The standard IFF form is as follows.

<Relation name=“goingTo”>

  <definition>

    <Expression>

      <Signature>

        <Person pos="1" var=“x” name="person"/>

        <City   pos="2" var=“y” name="city"/>

      </Signature>

      <Go><agent value="x"/><destination value="y"/></Go>

    </Expression>

  </definition>

</Relation>

An alternate abbreviated IFF form uses functional lambda expressions to define relations. Functional lambda expressions are typed lambda expressions with typed relational arguments. In other words, they are doubly typed lambda expressions.

<Relation name="goingTo">

  <sign pos="1" var="x" entity="Person>

  <sign pos="2" var="y" entity="City">

    <Go><agent value="x"/><destination value="y"/></Go>

  </sign>

  </sign>

</Relation>

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Please send questions, comments and suggestions about this page to: Robert E. Kent rekent@ontologos.org

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