Expression

IFF expressions are analogous to CG lambda expressions. For any natural number n an n-adic IFF expression has two parts: a signature and a body.

o The body is a logical expression in the ordinary sense, which is built up using the usual logical connectives and quantifiers. The natural number n is called the valence of the expression. The body has n entities designated as its formal parameters. The formal parameters are numbered from 1 to n, and each index between 1 and n identifies the formal parameter by position.

o The signature of the expression is a list (t₁, … , t_n), where each element t_i in the list is the entity type of the i-th formal parameter of the expression. In IFF the element t_i is of the form

<sign position="i" variable=“x” name="n" entity="t">

Since a 0-adic expression has no formal parameters, its signature is the empty sequence.

The most important observation is that expressions in the Information Flow Framework are regarded to be a special case of relation types.

The IFF expression element has three XML attributes: position, name and variable. The required position attribute and the optional name attribute have exactly the same function in expressions as they do in relation type declarations. The position attribute identifies the position of an argument in the list of all arguments, and hence serves as a local identifier. The name attribute offers an optional, but more mnemonic name for the argument when used in a record, or more generally, a relation instance. Neither of these is used in CG lambda expressions, probably because CG is a visually oriented notation. The required variable attribute is used in the same manner as the CG variable, serving as a line of identity between the signature and the body of an expression.

goingTo

Here is an example in CG and IFF of an expression 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.

CG

The CG linear form marks the parameters in terms of the Greek character l.

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

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

(lambda

(Person*x, City*y)

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

)

IFF

The standard IFF form is as follows.

<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>

The signature could also be expressed as follows.

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

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

author-publication

The following axiomatization in IFF represents the English sentence

“A person is an author of a document iff that document is a publication of that person.”

IFF

<Expression>

<comment>

A person is an author of a document iff

that document is a publication of that person.

</comment>

<Signature/>

<Forall var="p" entity=“Person">

<Forall var="d" entity=“Document">

<equiv>

<author person="p" document="d"/>

<publication document="d" person="p"/>

</equiv>

</Forall>

</Forall>

</Expression>

This is a closed expression, and has an empty signature. Using the binary transpose (involution) relation on the Relation type in the base IFF ontological language, the above axiom becomes the following much simpler specification.

<transpose relation1="author" relation2="publication"/>

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

Copyright © 2000 TOC (The Ontology Consortium). All rights reserved. Revised: July 2000