1

The logic of default inheritance in Word Grammar

Richard HudsonLexington, May 2012

2

Plan

1. Word Grammar 2. WG morphology3. Five problems for DI, and the WG

solutions4. Conclusions

3

1: Word Grammar

• Aims– to model language in cognition

• 'graceful integration'

– to discover if anything is unique to language• Assumptions

– cognition is a network– the network includes a taxonomy– the model must include processes as well as structures.

4

WG and language structure

• Language is a network• The network links sounds to meanings

– but NOT directly– so the units are not 'symbols' or 'constructions'

• The network defines:– 'levels'– various sub-taxonomies

5

'Levels' in a network

realization

pronunciation

morph

spelling

sound letter

concept

meaning

semantics

syntax

morphology

phon/graph-ology

word

morph

sound

6

Taxonomy in a network

concept

entity relation

letter wordmorphsound realization

pronunciation spelling

meaning

'is-a'

7

WG and processes

• Spreading activation– including attention

• Node-creation for tokens/exemplars– e.g. word-tokens in recognition or planning

• Binding– e.g. token to token in parsing

• Default inheritance

8

An example outside language: hearing some purring

cat

token 1

token 2?

binding

node-creation

purring

activationinheritance

token 3

purrer

9

An example inside language: hearing /kat/

CAT

realization

token 1

token 2?

/kat/

token 3

10

2: WG morphology

• Inferential and realizational• Morphosyntax

– words realized by meaningless morphs– any degree of generality

• word-class – lexeme – sub-lexeme

• Morphophonology– morphs realized by phones or letters

11

Morphosyntax in a network

word

adj-of

noun

BOYISH BOY plural

{boy}base

full

s-variant

inflectional morphology

A

full

base

adjective

derivational morphology

12

Morphophonology in a networkword {z}

bases-variant

{z}

1

2

pronunciation

/z//ɪ/

210 #

/s//ɪ/+1 #

sibilant

next

voiceless

next

13

3: Five problems for default inheritance

• The basic idea is very simple:– defaults generalise except when overridden

• But there are challenges:a. generality: going beyond morphologyb. reliability: non-monotonicityc. certainty: recognising clashes and winnersd. relevance: avoiding irrelevant enrichmente. economy: avoiding storage of outcomesf. sensibleness: avoiding silly categorization

14

DI in WG

• Since 1980 I've tried several different theories of DI– e.g. 1990: exceptions are marked with 'NOT …'

• 2007: A solution:– Default inheritance only applies to tokens. – DI is driven by spreading activation.– The network defines conflicts and outcomes.

15

a: Generality

• Default inheritance is part of general cognition.– Hence: prototype effects

• So the mechanism used for morphology must generalize – beyond ready-made AVMs– e.g. 'birds fly' but 'penguins don't fly'.

16

Generality in WG

• Properties are links to other concepts– not AVMs– e.g. 'Birds fly' is a property of 'bird' as well as

of 'fly'. – 'Not P' conflicts with 'P' and overrides it.

• 'not P' in a network: 'quantity of P = 0'

17

Penguins

bird

flier

flying

penguin

token

0#

0#

18

b: Reliability

• Monotonicity: inferences are– cumulative– reliable – i.e. not liable to later retraction

• But DI is non-monotonic– because default properties may be overridden– unless special ordering restrictions are imposed– but this is odd in a declarative system.

19

People or persons?noun

plural

full

s-variant

PERSON

PERSON, plural {people}

full

allows persons

20

Reliability in WG

• Inheritance only applies to tokens– i.e. at the foot of the taxonomy

• And it applies recursively working upwards– so the first value inherited is always the winner.

• So DI is, in fact, monotonic!• And DI is always part of the process of

node-building.

21

People, not personsnoun

plural

full

s-variant

PERSON

PERSON, plural {people}

full

token

22

c: Certainty

• Inheritable properties may be uncertain:– Multiple inheritance allows two outcomes.– A node's identity may be defined

• directly by a 'filler'• indirectly by reentrancy.

• In conflicts, which property wins?• WG: let the network decide.

23

Multiple inheritance

• No special provisions needed.• If conflicts arise, so be it.

– e.g. *I amn't• = BE, 1sg, negative• 1 sg: realization = {am}• negative: realization = {aren't}• unresolved because 1 sg and negative are sisters.

• Reentrancy (loops) is harder.

24

Is people the s-variant of PERSON?noun

plural x

full

s-variant

PERSON

PERSON, plural {person}

{z}2

1token y

Does token inherit s-variant?

If {person} isa x,

… and the consequences!

But if not,

then y inherits s-variant.

all is well.

25

Certainty in WG

• If: the inheritor for token x finds [X, R, Y]• = [X R Y] or [Y R X]• 'upper-case' dominates 'lower-case'

• And if:– x already has [x, r, …]

• then: Do nothing.– x already has [x, …, y]

• then: create [X, r, y], [r isa R]– otherwise: create [x, r, y], [r isa R], [y isa Y]

26

Certainty in a network

x

R

X Y

If: [X, R, Y]

and if: already [x, r, …]

Otherwise:create [x, r, y], [y isa Y], [r isa R]

Then: Do nothing.

Then: create [X, r, y], [r isa R]

Otherwise if: already [x, …, y]

and X dominates x

y

r

27

d: RelevanceThe inheritance explosion

• Each new node created is a token– so it inherits too, creating further nodes

• Every node in the taxonomy is an inheritance source.

• Every property can be inherited.• Inheritance is resource-intensive.

– E.g. 'Does a canary have skin?' takes longer to answer than 'Does a canary sing?'

• So we need a rationing mechanism.

28

Relevance in WG

• Do we inherit irrelevant properties?– e.g. spelling– etymology

• Relevance in WG:– only inherit active properties.– Activation levels vary, and reflect:

• past experience• present concerns

29

Context-dependent DI

school SCHOOL

etymology

skhole

meaning

token

Assume: Total inheritance.Relevant inheritance.

30

e: Economy

• Do we store inherited properties?– Not in general.– Mixture of full and empty entries.

• Economy in WG: Only tokens inherit– So types aren't enriched.– But tokens may become types

• i.e. may be 'learned'

31

Fringe activityMemorychanges slowly

Experiencechanges

fast

32

f: sensibleness

• Problem: How to avoid silly classification?– e.g. a block of wood isa bird, but overrides all

bird properties.• Solution: A theory of learning and use:

– We only build isa links where properties are shared:

• in creating new category nodes• in creating new token nodes.

33

5: Conclusions

• DI is part of cognition.– and needs a cognitive model– it mustn't be limited to AVMs.

• It's part of token-building.– so it's monotonic.

• It's limited to active relations.– so it only inherits what's relevant.

34

Thank you

• This slideshow can be downloaded from:www.phon.ucl.ac.uk/home/dick/talks.htm

• For more on Word Grammar, see:www.phon.ucl.ac.uk/home/dick/wg.htm