Moving toward formalisation COMP60421 Sean Bechhofer - - PowerPoint PPT Presentation

Moving toward formalisation COMP60421

Sean Bechhofer sean.bechhofer@manchester.ac.uk

• (thanks to Bijan Parsia for slides)

Previously...

• We started the acquisition process...

– We elicited tacit knowledge – In a variety of ways – about a set of terms (or concepts)

• But even there we could get more explicit

– Normalising terms (e.g., “symmetry or symmetric”?) – Hierarchy (and other direct relations between terms) – Categorizing terms (e.g., as modifiers or self-standing) – Constraining and defining terms

• 2 important next steps

– Getting even more explicit and precise

• Refining our proto-represntation

– Getting actionable

• Building a representation

Term extraction

• Let’s consider a simple text passage:

– There are several sorts of domesticated animals, though by far the most are mammals (like us!). For example, our faithful pets, cats and dogs, are clearly domesticated (or we would not keep such dangerous carnivores in our homes), as is the delicious cow which is farmed in ever increasing numbers.

Term extraction

• Highlighting!

– There are several sorts of domesticated animals, though by far the most are mammals (like us!). For example, our faithful pets, cats and dogs, are clearly domesticated (or we would not keep such dangerous carnivores in our homes), as is the delicious* yet docile cow which is farmed in ever increasing numbers.

*Note that Bijan is a vegetarian! But he does remember some exceeding delicious cows.

Term extraction

• We pull these out

– domesticated – animals – mammals – us – pets – cats – dogs – dangerous – carnivores – homes – delicious – cow – farmed – increasing – numbers

Term extraction

• We pull these out

– domesticated – animals – mammals – us – pets – cats – dogs – dangerous – carnivores – homes – delicious – cow – farmed – increasing – numbers

These are quite odd but in different ways

Term extraction

• We pull these out

– domesticated – animals – mammals – us – pets – cats – dogs – dangerous – carnivores – homes – delicious – cow – farmed – increasing – numbers

These are similar but have different levels

• f generality, and non-

standard spelling

Grouping

• Base animal categories (nouny terms)

– animals – cats – dogs – mammals – cow – us

• Ways an animal can be (adjectivally terms)

– domesticated – pets – dangerous – carnivores – delicious – farmed

• Stuff

– homes – increasing – numbers

Grouping

• Base animal categories (nouny terms)

– animals – cats – dogs – mammals – cow – us

• Ways an animal can be (adjectivally terms)

– domesticated – pets – dangerous – carnivores – delicious – farmed

• Stuff

– homes – increasing – numbers

Should we care about these?

A key slogan

• Representations are

– context sensitive, and – interest relative

• Context sensitive?

– Application or kind of application

• Interests?

– Application needs

• Teaching, categorising, data acquisition

– Audience

• Children, lay people, different disciplines, clinicians vs. researchers
• Establish context and relevant interests

– In this case the context is this class and my interests are working up a reasonable example

Grouping

• Base animal categories (nouny terms)

– animals – cats – dogs – mammals – cow – us

• Ways an animal can be (adjectivally terms)

– domesticated – pets – dangerous – carnivores – delicious – farmed

• Stuff

– homes – increasing – numbers

Should we care about these? No! (Why?)

Normalise Terms!

• Base animal categories (nouny terms)

– animals – cats – dogs – mammals – cow – us

• Ways an animal can be (adjectivally terms)

– domesticated – pets – dangerous – carnivores – delicious – farmed

Standardise number

Normalise Terms!

• Base animal categories (nouny terms)

– Animal – Cat – Dog – Mammal – Cow – us

• Ways an animal can be (adjectivally terms)

– domesticated – pets – dangerous – carnivores – delicious – farmed

Make explicit

Normalise Terms!

• Base animal categories (nouny terms)

– Animal – Cat – Dog – Mammal – Cow – Human

• Ways an animal can be (adjectivally terms)

– domesticated – pets – dangerous – carnivores – delicious – farmed

These seem extra (not of interest), and we can adjectivize the rest

Normalise Terms!

• Base animal categories (nouny terms)

– Animal – Cat – Dog – Mammal – Cow – Human

• Ways an animal can be (adjectivally terms)

– Domesticated – Pet – Carnivorous – Farmed

We have some background knowledge we can use to “round out” these terms

Normalise Terms!

• Base animal categories (nouny terms)

– Animal – Cat – Dog – Mammal – Cow – Human

• Ways an animal can be (adjectivally terms)

– Domesticated – Pet – Farmed – Wild – Carnivorous – Herbivorous – Omnivorous

We have some background knowledge we can use to “round out” these terms (using elicitation techniques)

Organise terms

• Base animal categories (nouny terms)

– General

• Animal
• Mammal

– Specific

• Cat
• Dog
• Cow
• Human
• Ways an animal can be (adjectivally terms)

– General

• Domesticated
• Wild
• Carnivorous
• Herbivorous
• Omnivorous

– Specific

• Pet
• Farmed

Both General and Specific Contraries! Contraries?

Organise terms

• Self-Standing (nouny terms)

– General

• Animal
• Mammal

– Specific

• Cat
• Dog
• Cow
• Human
• Modifiers (adjectivally terms)

– General

• Domesticated
• Wild
• Carnivorous
• Herbivorous
• Omnivorous

– Specific

• Pet
• Farmed

What terms are definable?

Organise terms

• Self-Standing (nouny terms)

– General

• Animal
• Mammal

– Specific

• Cat
• Dog
• Cow
• Human
• Modifiers (adjectivally terms)

– General

• Domesticated
• Wild
• Carnivorous
• Herbivorous
• Omnivorous

– Specific

• Pet
• Farmed

“An animal which eats only meat”

What terms are definable?

Existing term New terms

Capturing in an actionable form

• We can capture what we’ve done

– in a structured way – and get some benefits!

Iterative process

• Building the representation is informative

– Definitions elicit new terms – Interests and Context tell us when a fixed point is reached

• Fatigue! Fatigue works...
• Until now, entirely human process

– Having the structured form helps a little

• Easier search/browsing

– But no “content” feedback – For this, we need to understand

• what we want to represent
• what we can represent!

So far...

• We are well into KA

– Term extraction – Initial regimentation

• Normalisation
• Hierarchical organisation
• Categorisation

– Started additional capture

• Adding definitions
• Ready to consider the next step

– Proto-Formalisation!

• Remember:

– Interest sensitive and context relative – We’re looking for benefits (to way against costs)

• But first...

22

Remember our passage

• With highlighting!

– There are several sorts of domesticated animals, though by far the most are mammals (like us!). For example, our faithful pets, cats and dogs, are clearly domesticated (or we would not keep such dangerous carnivores in our homes), as is the delicious yet docile cow which is farmed in ever increasing numbers.

• Why not:

– There are several sorts of domesticated animals, though by far the most are mammals (like us!). For example, our faithful pets, cats and dogs, are clearly domesticated (or we would not keep such dangerous carnivores in our homes), as is the delicious yet docile cow which is farmed in ever increasing numbers.

23

What terms should go in?

• It depends!

– Interests and context – Resources, including

• Time
• Energy
• Representational capabilities
• Skill, etc.
• Fewer than all

– A generally good rule of thumb

• Other than what’s there

– Another good rule of thumb! – “Fleshing out”

• Organisational needs (e.g., “LivingThing”)
• Representational needs (e.g., “eats”)
• Coverage, “completeness” (e.g., “omnivore”)

24

What matters? How do we tell?

Symmetry in biology is the balanced distribution of duplicate body parts or shapes. The body plans of most multicellular organisms exhibit some form of symmetry, either radial symmetry orbilateral symmetry or "spherical symmetry". A small minority exhibit no symmetry (are asymmetric).

• In nature and biology, symmetry is approximate. For example, plant

leaves, while considered symmetric, will rarely match up exactly when folded in half.

25

What terms are definable?

• Self-Standing (nouny terms)

– General

• Animal
• Mammal

– Specific

• Cat
• Dog
• Cow
• Human
• Modifiers (adjectivally terms)

– General

• Domesticated
• Wild
• Carnivorous
• Herbivorous
• Omnivorous

– Specific

• Pet
• Farmed
• New Terms

26

What terms are definable?

• Self-Standing (nouny terms)

– General

• Animal
• Mammal

– Specific

• Cat = only eats dogs
• Dog = eats cats
• Cow = vegetarian like Bijan
• Human = eats anything (but not cats and dogs)
• Modifiers (adjectivally terms)

– General

• Domesticated
• Wild
• Carnivorous = eats meat
• Herbivorous = eats plants
• Omnivorous = eats plans and meat

– (= is both a carnivore and an herbivore)

– Specific

• Pet
• Farmed
• New Terms

????

• nly?

eats? both? Bijan?

27

First Regiment!

• Self-Standing (nouny terms)

– General

• Animal
• Mammal

– Specific

• Cat = eats dogs
• Dog = eats cats
• Cow = eats plants
• Human = eats both plants and meat
• Modifiers (adjectivally terms)

– General

• Domesticated
• Wild
• Carnivorous = eats meat
• Herbivorous = eats plants
• Omnivorous = both a carnivore and an herbivore)

– Specific

• Pet
• Farmed
• New Terms

????

• nly?

eats? both? Bijan?

28

Regimented?

• Self-Standing (nouny terms)

– General

• Animal
• Mammal

– Specific

• Cat = eats dogs
• Dog = eats cats
• Cow = eats plants
• Human = eats both plants and meat
• Modifiers (adjectivally terms)

– General

• Domesticated
• Wild
• Carnivorous = eats meat
• Herbivorous = eats plants
• Omnivorous = both a carnivore and an herbivore)

– Specific

• Pet
• Farmed
• New Terms

????

• nly?

eats? both? Bijan? Ambiguous! Are these really definitions? Normalise!

29

Regimented!

• Self-Standing (nouny terms)

– General

• Animal
• Mammal

– Specific

• Cat = eats only Dog
• Dog = eats Cat
• Cow = eats Plant
• Human = eats Plants and Meat
• Modifiers (adjectivally terms)

– General

• Domesticated
• Wild
• Carnivorous = eats only Meat
• Herbivorous = eats only Plants
• Omnivorous = Carnivorous and Herbivorous

– Specific

• Pet
• Farmed
• New Terms

eats

• nly

Plant and Meat Are all these necessary?

30

Pruned!

• Self-Standing (nouny terms)

– General

• Animal
• Mammal

– Specific

• Cat = eats only Dog
• Dog = eats Cat
• Cow = eats not Animal
• Human = eats not Animal and Animal
• Modifiers (adjectivally terms)

– General

• Domesticated
• Wild
• Carnivorous = eats only Animal
• Herbivorous = eats only not Animal
• Omnivorous = Carnivorous and Herbivorous

– Specific

• Pet
• Farmed
• New Terms

eats

• nly

and not

Domain specific “Logicy”

Still too strong! Repetitive!

31

Pruned!

• Self-Standing (nouny terms)

– General

• Animal
• Mammal

– Specific

• Cat = eats only Dog
• Dog = eats Cat
• Cow SubClassOf eats not Animal
• Human SubClassOf eats not Animal and Animal
• Modifiers (adjectivally terms)

– General

• Domesticated
• Wild
• Carnivorous = eats only Animal
• Herbivorous = eats only not Animal
• Omnivorous = Carnivorous and Herbivorous

– Specific

• Pet
• Farmed
• New Terms

eats

• nly

and not SubClassOf

Domain specific “Logicy”

32

We’re ready to formalise!

33

Underlying Language

Class: Cat Annotations: rdfs:comment "eats only Dog", rdfs:comment "Definable", rdfs:comment "SelfStanding" EquivalentTo: eats only Dog SubClassOf: Mammal

(There are many possible syntaxes!)

34

Recall the regimentation

• Self-Standing (nouny terms)

– General

• Animal

– Mammal » Cat = eats only Dog » Dog = eats only Cat » Cow SubClassOf eats only not Animal » Human SubClassOf eats 


• nly not Animal and Animal
• Modifiers (adjectivally terms)

– Domesticated

• Pet
• Farmed

– Wild – Carnivorous = eats only Animal – Herbivorous = eats only not Animal – Omnivorous = Carnivorous and Herbivorous

• New Terms

eats

• nly

and not SubClassOf

Domain specific “Logicy”

35

Recall the (Proto)Formalisation

Class: Cat Annotations: rdfs:comment "eats only Dog", rdfs:comment "Definable", rdfs:comment "SelfStanding" EquivalentTo: eats only Dog SubClassOf: Mammal

36

(don’t look here)

Kind and Name of Term “Mere” Comments

(Their content is significant, but outside our formalism.)

(Hierarchical) Relation to Another Term

“Minimal”

Meaning? (Semantics)

Class: Cat Annotations: rdfs:comment "eats only Dog", rdfs:comment "Definable", rdfs:comment "SelfStanding" EquivalentTo: eats only Dog SubClassOf: Mammal

37

(don’t look here)

A set of entites Nothing! A sub-super set relation (The set of cats is a subset of the set of mammals.)

These are just intuitions!

Benefits?

Class: Cat Annotations: rdfs:comment "eats only Dog", rdfs:comment "Definable", rdfs:comment "SelfStanding" EquivalentTo: eats only Dog SubClassOf: Mammal

38

(don’t look here)

• Some structure

– We can retrieve classes – We can search for “comments” – We can represent hierarchy in a number of ways

Side note: A “Computer View”

Class: G1 Annotations: rdfs:comment «65 61 74 73 20 6F 6E 6C 79 20 44 6F 67» rdfs:comment «44 65 66 69 6E 61 62 6C 65», rdfs:comment «53 65 6C 66 53 74 61 6E 64 69 6E 67» EquivalentTo: eats only Dog SubClassOf: G2

39

(don’t look here)

Doing Better (in a simple way)!

Class: Cat Annotations: definition "eats only Dog", isDefinable True, grammaticalType SelfStanding EquivalentTo: eats only Dog SubClassOf: Mammal

40

(don’t look here)

This is still unstructured! Add structure! (ease data entry, retrieval)

Doing Better!

Class: Cat Annotations: rdfs:comment "eats only Dog", isDefinable True, grammaticalType SelfStanding EquivalentTo: eats only Dog SubClassOf: Mammal

41

(don’t look here)

Pull this out!

Doing Better

Class: Cat Annotations: rdfs:comment "eats only Dog", rdfs:comment "Definable", rdfs:comment "SelfStanding" EquivalentTo: eats only Dog SubClassOf: Mammal

42

And put it here!

Meaning? (Semantics)

Class: Cat Annotations: rdfs:comment "eats only Dog", rdfs:comment "Definable", rdfs:comment "SelfStanding" EquivalentTo: eats only Dog SubClassOf: Mammal

43

A set of entites Still Nothing! A sub-super set relation EquivalentTo is easy... What about the expression?

We Need a Syntax!

• A simple grammar for expressions (aka, descriptions)
• Examples

– Animal that eats only Animal – eats some (not Animal) – not (eats only Animal and some Animal)

44

atomicClass ::= [A-Z][a-zA-Z]* (in camel case) atomicProperty ::= [a-z][a-zA-Z]* (in camel case) description ::= conjunction 'or' conjunction { 'or' conjunction } | conjunction conjunction ::= classIRI 'that' [ 'not' ] restriction { 'and' [ 'not' ] restriction } | primary 'and' primary { 'and' primary } | primary primary ::= [ 'not' ] ( restriction | atomic ) restriction ::= property 'some' primary | property 'only' primary

Grammar is a slightly modified subset of the one given in: http://www.w3.org/TR/owl2-manchester-syntax/

Bit More Syntax!

• A simple grammar for axioms (aka propositions)
• Examples

– Class: CarnivorousAnimal EquivalentTo: Animal that eats only Animal – Class: Cow SubClassOf: eats some (not Animal) – ConfusedCow SubClassOf: not (eats only Animal and some Animal)

• (I omit the leading “Class:” where unambiguous.)
• What does it all mean!?
• Coming next…

45

classFrame ::= 'Class:' atomicClass { 'Annotations:' annotation { ',' annotation } | 'SubClassOf:' description { ',' annotation } | 'EquivalentTo:' description { ',' annotation }

Semantics (semi-formal)!

• Expressions

– atomic classes name sets of entities – properties describe binary relations – descriptions describe sets of entities

• desc1 and desc2 ☞ the set s.t. both desc1 and desc2 are true
• desc1 or desc2 ☞ the set s.t. either desc1 or desc2 are true
• property some desc ☞ the set s.t. they are related by the property to at

least one desc

• property only desc ☞ the set s.t. all the things they are related to by the

property are desc

• not desc ☞ the set s.t. desc is not true
• Axioms are true or false

– A SubClassOf: desc ☞ is true iff every member of A is desc – A EquivalentTo: desc ☞ is true iff A is the same set as desc

46

Exploring Benefits

• Omnivorous

– Annotations: comment "Carnivorous and Herbivorous"

• Annotations have no meaning! (to the renderer)

47

Exploring Benefits

• Omnivorous

– EquivalentTo: Carnivorous and Herbivorous

• Expressions have meaning! (to the renderer)

48

Is this right?

Can We Get More?

• Given

– Carnivorous EquivalentTo eats only Animal – Dog EquivalentTo: eats only Cat – Cat EquivalentTo: eats only Dog

• What “should” happen?

49

Clearly wrong!

• Consider:

– Human SubClassOf: eats 


• nly (not Animal and Animal)

– What’s wrong with this?

Oh, the Humanity!

50

Bad, but not as bad as one might expect

• Consider:

– Human SubClassOf: eats 
 some (not Animal and Animal) – What’s wrong with this?

An alternative definition

51

Benefits!

• Links for “free”

– Tools make implicit links explicit – We don’t have to encode every link ourselves – Different modality

• Instead of generalisation relations...focus on meanings
• Local rather than global
• Verification

– Definitions have consequences

• Wrong links
• Detectable problems

– Links so wrong they are never right

52