Moving toward formalization

Bijan Parsia

Last class...

We started the acquisition process...

We elicitated tacit knowledge

In a variety of ways

about a set of terms (or concepts)

But even there we could be more explicit

Hierarchy (and other direct relations between terms)
Categorizing terms (e.g., modifers)
Constraining and defining terms

2 importent next steps

Getting even more explicit
Getting computational

Getting more explicit

Let's draw!

Nodes (with labels) "represent" terms
Arcs "represent"some relationship (default to IS-A)
Reading: What IS-A Is and Isn't: An Analysis of Taxonomic Links in Semantic Networks

Now that we have a representation, what can it do for us?

IS-A ambiguities

Two kinds of term

Classes
Individuals

IS-A as subsumption

Cat IS-A Animal
Cat subClassOf Animal

IS-A as instantiation

Fred IS-A Cat

Fred instance-of Cat

Fred type/has-type Cat

Simplest way to resolve

Have different labels for difference arcs

Note that with loss of ambiguity, loss of expressiveness!
What kind of expressiveness?

We have 4 possible patterns:

Class-Class

sub-class relation

Instance-Class

instance/member of relation

Instance-Instance

Arbitrary relation

E.g., eats, loves, teaches

Class-Instance (??)

Current Limits on Subsumption

What kind of reasoning can we do?

Given a set of classes and some subclass axioms...what's implicit?
How might we detect this?
How might we achieve desired effects?

If we have a complex set of subsumption
How might we want to describe classes?

In terms of other classes?

Interlude: What is a Taxonomy?

General Notion

An organization (typically hierarchial) of (kinds of) entities

E.g., Kingdom-phyla-class-order-family-genus-species

I.e., subclass relations
Along with principles of organization

Think of the biological..some notion of relatedness
Self-standing vs. modifer (i.e., different facets)

In computer science, often refers to a subsumption heirarchy

esp. if asserted
Think Yahoo!, DMoz, even library of congress
Connected with "semantic nets"

Animal Taxonomy

Animal

Mammal

Cat
Dog
Cow
Person

Domestic

Pet

Cat
Dog

Farmed

Cow

Problems with Taxonomies?

Organizationally rigid

To be in it's proper place, you must put it there
If there are multiple proper places...put 'em!

Easier for leaves, harder for multiple organizations
See: Metacrap: Putting the torch to seven straw-men of the meta-utopia

Esp. 2.5 and 2.7

Impoverished description

that cats are carnivores
but not, why cats are carnivores
or, what it is to be a carnivore
or even, if we say that cats are carnivores and herbivores, there's a problem!

More expressivity

Not just term-term relations
We add definitions

a carnivore is an animal that eats only meat

We add constraints

carnivores are not herbivores

What entailments might we hope for?

From, carnivores eat only meat
And, cats eat only mice
And, mice are meat
That, cats are carnivores

Some descriptive vocabulary

Operator	Example
CLASS1 and CLASS2	Cat and Female
CLASS1 or CLASS2	Male or Female
not CLASS	not Female
PROPERTY some CLASS	loves some Cat
PROPERTY only CLASS	loves only Cat

(This is a fragment of the Manchester OWL Syntax.)

These form class descriptions or class expressions. We can use them anywhere we'd use a named class.
(That is, they can be node labels.)

What does it mean?

We've given some intuitive readings
We can consider what entailments we want to permit
Then we can formalize this language

This will come in the FOL section

It's worth trying to find things you want to say

and what you want to follow from that

Think about this vocabulary when doing your definitions

but don't (yet) be bound by them