Theory

Information Flow Foundation

A theory is a pair T = átyp(T), ⊢_Tñ, where typ(T) is a set (of types) and ⊢_T is a binary relation on the powerset of typ(T) called consequence. An element in the consequence relation, which is denoted as a sequent Γ ⊢_T Δ and is called a constraint, has the logical intention "G → $D that “if all types in G hold then some type in D holds.” When typ(A) = typ(T) for classification A, an instance a Î inst(A) satisfies this constraint when it satisfies the intention: if instance a is of every type in Γ, then it is of some type in Δ. The theories generated by classifications (using satisfaction) obey structural axioms, such as identity, weakening, and cut.

In the Information Flow Framework theories are analogous to ontologies. However, they differ from ontologies in two respects: they have no relation, but are only concerned with entities; the constraints are restricted to sequents.

Color Theory

The following example specifies a "controlled vocabulary" in IFF. This “nominal” theory of Information Flow represents a (rather limited) collection of color terms. By a nominal theory we mean part of the extent a higher-order genus type. The types within the theory are automatically instances of the genus type of the theory: "species instance of genus". For example, "the color red" is a "color".

“Rainbow Colors = {red, orange, yellow, green, blue, indigo and violet}.”

IFF

Theory

(located at located at the address http://www.color.org/theory/Rainbow/)

The example below illustrates a theory and a language embedded within the theory.

<IFF>

<Theory id="Rainbow" genus="Color">

<language>

<Language>

<Entity name="red"/>

<Entity name="orange"/>

<Entity name="yellow"/>

<Entity name="green"/>

<Entity name="blue"/>

<Entity name="indigo"/>

<Entity name="violet"/>

</Language>

</language>

<partition>

<red/><orange/><yellow/><green/><blue/><indigo/><violet/>

</partition>

</Theory>

</IFF>

Of course, at some point we may decide that these are not enough colors. Say we also need a black color and a white color.

“Day-Nite Colors = Rainbow Colors + {black, white}.”

Then we merely extend the above theory to include these new colors. This extension theory might be located in the above Color ontology or it might be located in a separate ontology (as below) that extends the Color ontology.

Theory

<IFF>

<Theory id="Day-Nite" genus="color"/>

<extends href="http://www.ontologos.org/iff/ontology/"/>

<extends theory="Rainbow" href="http://www.color.org/theory/Rainbow/"/>

<language>

<Language>

<Entity name="white"/>

<Entity name="black"/>

</Language>

</language>

<partition>

<Rainbow:red/><Rainbow:orange/><Rainbow:yellow/><Rainbow:green/>

<Rainbow:blue/><Rainbow:indigo/><Rainbow:violet/><white/><black/>

</partition>

</Theory>

</IFF>

Movie Genre Theory

The following example specifies another "controlled vocabulary" in IFF. This theory represents the controlled vocabulary used by the Internet Movie Database to describe movie genre. Movie genres are listed in the following textual description. No constraints between genres are specified. As a result, this generates the smallest Information Flow theory on the set of genre.

“Genre

=

{Action, Adventure, Animation, Children's, Comedy, Crime, Documentary, Drama, Film-Noir, Horror, Musical, Mystery, Romance, Sci-Fi, Thriller, War, Western}.”

IFF

Theory

<IFF>

<Theory genus="Genre">

<extends href="http://www.ontologos.org/IFF/ontology/"/>

<language>

<Language>

<Entity name="Action"/>

<Entity name="Adventure"/>

<Entity name="Animation"/>

<Entity name="Children's"/>

<Entity name="Comedy"/>

<Entity name="Crime"/>

<Entity name="Documentary"/>

<Entity name="Drama"/>

<Entity name="Film-Noir"/>

<Entity name="Horror"/>

<Entity name="Musical"/>

<Entity name="Mystery"/>

<Entity name="Romance"/>

<Entity name="Sci-Fi"/>

<Entity name="Thriller"/>

<Entity name="War"/>

<Entity name="Western"/>

</Language>

</language>

</Theory>

</IFF>

Protein Feature Theory

This theory models a “controlled vocabulary’ in a pharmacological knowledgebase. The terms in the controlled vocabulary are features of proteins. This example illustrates the use of the common XML attribute, when a common terminology is desired in addition to a technical terminology.

This representation can be specified from scratch, or it can be the result of the conceptual scaling process being applied to one of the other representations: a collective designator, a collection of values, or a collection of instances. The scaling of an unordered set is called nominal conceptual scaling, whereas the scaling of a total order is either ordinal scaling or interordinal scaling.

IFF

Theory

<IFF>

<Theory genus="Protein_Feature">

<extends href="http://www.ontologos.org/IFF/ontology/"/>

<language>

<Language>

<Entity name="Western"/>

<Entity name=“act_site" common=“active site"/>

<Entity name=“binding" common=“binding site"/>

<Entity name=“ca_bind" common=“calcium binding site"/>

<Entity name=“carbohyd" common=“"/>

<Entity name=“conflict" common=“"/>

<Entity name=“disulfid" common=“disulfide bond"/>

<Entity name=“dna_bind" common=“"/>

<Entity name=“domain" common=“"/>

<Entity name=“helix" common=“alpha helix"/>

<Entity name=“init_met" common=“"/>

<Entity name=“lipid" common=“"/>

<Entity name=“metal" common=“"/>

<Entity name=“mod_res" common=“"/>

<Entity name=“mutagen" common=“"/>

<Entity name=“non_cons" common=“non-conserved"/>

<Entity name=“non_ter" common=“"/>

<Entity name=“np_bind" common=“"/>

<Entity name=“peptide" common=“"/>

<Entity name=“propep" common=“"/>

<Entity name=“repeat" common=“"/>

<Entity name=“signal" common=“signal domain"/>

<Entity name=“similar" common=“"/>

<Entity name=“site" common=“"/>

<Entity name=“strand" common=“beta strand"/>

<Entity name=“thioeth" common=“"/>

<Entity name=“thiolest" common=“"/>

<Entity name=“transit" common=“"/>

<Entity name=“transmem" common=“transmembrane"/>

<Entity name=“turn" common=“"/>

<Entity name=“unsure" common=“"/>

<Entity name=“variant" common=“variant residue"/>

<Entity name=“varsplice" common=“"/>

<Entity name=“zn_fing" common=“zinc finger"/>

</Language>

</language>

</Theory>

</IFF>

RSACi Rating Ontology

Ontologies often serve as containers of theories, especially when controlled vocabularies are being used. The following example, which illustrates an ontology containing several theories, specifies another "controlled vocabulary" in IFF. Each embedded Information Flow theory, which represents an RSACi rating, is specified as an ordinal theory (a total order, in this case).

“The RSACi ratings must be one of five levels {0, 1, 2, 3, 4}.”

IFF

Ontology

<IFF>

<Ontology id="RSACi" version="1.0">

<extends href="http://www.ontologos.org/iff/ontology/"/>

<Entity name="Rating"/>

<Entity name="Rating.Violence"/>

<Entity name="Rating.Nudity"/>

<Entity name="Rating.Sex"/>

<Entity name="Rating.Language"/>

<subtype specific="Rating.Violence" generic="Rating"/>

<subtype specific="Rating.Nudity" generic="Rating"/>

<subtype specific="Rating.Sex" generic="Rating"/>

<subtype specific="Rating.Language" generic="Rating"/>

…

<Theory genus="Rating.Violence">

...

</Theory>

<Theory genus="Rating.Nudity">

...

</Theory>

<Theory genus="Rating.Sex">

...

</Theory>

<Theory genus="Rating.Language">

<language>

<Language>

<Entity name="Level4"/>

<comment>Crude, vulgar language or extreme hate speech</comment>

<Entity name="Level3"/>

<comment>Strong language or hate speech</comment>

<Entity name="Level2"/>

<comment>Moderate expletives or profanity</comment>

<Entity name="Level1"/>

<comment>Mild expletives</comment>

<Entity name="Level0"/>

<comment>None of the above</comment>

</Language>

</language>

<subtype specific="Level0" generic="Level1"/>

<subtype specific="Level1" generic="Level2"/>

<subtype specific="Level2" generic="Level3"/>

<subtype specific="Level3" generic="Level4"/>

</Theory>

</Ontology>

</IFF>

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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