The logic of default inheritance in Word Grammar

1. The logic of default inheritance in Word Grammar Richard Hudson Lexington, May 2012

2. Plan • Word Grammar • WG morphology • Five problems for DI, and the WG solutions • 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 concept semantics meaning syntax word realization morph morph morphology spelling pronunciation phon/graph-ology sound letter sound

6. Taxonomy in a network concept 'is-a' relation entity meaning realization sound morph letter word pronunciation spelling

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 purrer purring cat binding ? token 2 token 1 token 3 inheritance activation node-creation

9. An example inside language: hearing /kat/ realization /kat/ CAT ? token 2 token 1 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 inflectional morphology derivational morphology base word A full adjective noun full BOYISH BOY plural adj-of s-variant base {boy}

12. Morphophonology in a network pronunciation word {z} 2 1 base # 0 s-variant /z/ /ɪ/ 1 # 1 2 {z} /s/ /ɪ/+ next next voiceless sibilant

13. 3: Five problems for default inheritance • The basic idea is very simple: • defaults generalise except when overridden • But there are challenges: • generality: going beyond morphology • reliability: non-monotonicity • certainty: recognising clashes and winners • relevance: avoiding irrelevant enrichment • economy: avoiding storage of outcomes • 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 flier flying bird # 0 penguin # 0 token

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? allows persons noun full PERSON plural s-variant full {people} PERSON, plural

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 persons noun full plural PERSON s-variant full PERSON, plural {people} 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? Does token inherit s-variant? noun full If {person} isa x, then y inherits s-variant. plural PERSON x s-variant … and the consequences! all is well. But if not, PERSON, plural {person} {z} 2 y token 1

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 and X dominates x If: [X, R, Y] R and if: already [x, r, …] X Y Then: Do nothing. Otherwise if: already [x, …, y] Then: create [X, r, y], [r isa R] r Otherwise: x y create [x, r, y], [y isa Y], [r isa 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 meaning etymology skhole SCHOOL school token Total inheritance. Assume: 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 activity Memory changes slowly Experience changes 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