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

2 Plan 1.Word Grammar 2.WG morphology 3.Five problems for DI, and the WG solutions 4.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 letterwordmorphsound 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 activation inheritance 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 network word {z} base s-variant {z} 1 2 pronunciation /z/ /ɪ//ɪ/ # /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 morphology b.reliability: non-monotonicity c.certainty: recognising clashes and winners d.relevance: avoiding irrelevant enrichment e.economy: avoiding storage of outcomes f.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 persons noun 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 1 token 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: Relevance The 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 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: For more on Word Grammar, see: