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Feature structures and unification

Feature structures and unification. Attributes and values. Attributes and values. The following object describes a class of persons:. Attributes and values. The following object describes a class of persons: age 22 gender M nationality Norwegian. Attributes and values.

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Feature structures and unification

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  1. Feature structures and unification

  2. Attributes and values

  3. Attributes and values The following object describes a class of persons:

  4. Attributes and values The following object describes a class of persons: age 22 gender M nationality Norwegian

  5. Attributes and values The following object describes a class of persons: age 22 gender M nationality Norwegian Attributes

  6. Attributes and values The following object describes a class of persons: age 22 gender M nationality Norwegian Values Attributes

  7. Attributes and values The following object describes a class of persons: age 22 gender M nationality Norwegian Let this be the class of persons described:

  8. Attributes and values The following object describes a class of persons: age 22 gender M nationality Norwegian Let this be the class of persons described:

  9. Attributes and values The following object describes a class of persons: age 22 gender M nationality Norwegian Let this be the class of persons described: Then remove a feature...

  10. Attributes and values The following object describes a class of persons: age 22 nationality Norwegian Let this be the class of persons described: Then remove a feature...

  11. Attributes and values The following object describes a class of persons: age 22 nationality Norwegian Let this be the class of persons described: Then remove a feature... and the class grows.

  12. Attributes and values The following object describes a class of persons: age 22 nationality Norwegian Let this be the class of persons described: Then remove a feature... and the class grows. Add a feature instead...

  13. Attributes and values The following object describes a class of persons: age 22 gender M nationality Norwegian eyecolour brown Let this be the class of persons described: Then remove a feature... and the class grows. Add a feature instead...

  14. Attributes and values The following object describes a class of persons: age 22 gender M nationality Norwegian eyecolour brown Let this be the class of persons described: Then remove a feature... and the class grows. Add a feature instead... and the class shrinks.

  15. Attributes and values The following object describes a class of persons: age 22 gender M nationality Norwegian A grammar example:

  16. Attributes and values The following object describes a class of persons: age 22 gender M nationality Norwegian A grammar example: cat NP number sg person 3

  17. Attributes and values The following object describes a class of persons: age 22 gender M nationality Norwegian A grammar example: cat NP number sg person 3 This object describes a class of phrases:

  18. Attributes and values The following object describes a class of persons: age 22 gender M nationality Norwegian A grammar example: cat NP number sg person 3 This object describes a class of phrases: a man the horse some red car the King’s man water nice beer ...

  19. Attributes and values The following object describes a class of persons: age 22 gender M nationality Norwegian A grammar example: cat NP number sg person 3 This object describes a class of phrases: Remove a feature... a man the horse some red car the King’s man water nice beer ...

  20. Attributes and values The following object describes a class of persons: age 22 gender M nationality Norwegian A grammar example: cat NP person 3 This object describes a class of phrases: Remove a feature... a man the horse some red car the King’s man water nice beer ...

  21. Attributes and values The following object describes a class of persons: age 22 gender M nationality Norwegian A grammar example: cat NP person 3 This object describes a class of phrases: Remove a feature... and the class grows. men the horses some red cars the King’s men waters nice beers ... a man the horse some red car the King’s man water nice beer ...

  22. Feature structures as functions cat NP number sg person 3 f1:

  23. Feature structures as functions cat NP number sg person 3 f1: • A set of ordered pairs (of attributes and values)

  24. Feature structures as functions cat NP number sg person 3 f1: • A set of ordered pairs (of attributes and values) • Never more than one occurrence of a given attribute

  25. Feature structures as functions cat NP number sg person 3 f1: • A set of ordered pairs (of attributes and values) • Never more than one occurrence of a given attribute • Never more than one value of a given attribute (but different attributes can have the same value)

  26. Feature structures as functions cat NP number sg person 3 f1: • A set of ordered pairs (of attributes and values) • Never more than one occurrence of a given attribute • Never more than one value of a given attribute (but different attributes can have the same value) • Hence such a structure can be considered asa function from attributes to values

  27. Feature structures as functions cat NP number sg person 3 f1: • A set of ordered pairs (of attributes and values) • Never more than one occurrence of a given attribute • Never more than one value of a given attribute (but different attributes can have the same value) • Hence such a structure can be considered asa function from attributes to values • Example: • f1(cat)=NP • f1(number)=sg • f1(person)=3

  28. Feature structures as functions cat NP number sg person 3 f1: • A set of ordered pairs (of attributes and values) • Never more than one occurrence of a given attribute • Never more than one value of a given attribute (but different attributes can have the same value) • Hence such a structure can be considered asa function from attributes to values • Example: • f1(cat)=NP • f1(number)=sg • f1(person)=3 • Values can be atomic or complex:

  29. Feature structures as functions cat NP number sg person 3 f1: • A set of ordered pairs (of attributes and values) • Never more than one occurrence of a given attribute • Never more than one value of a given attribute (but different attributes can have the same value) • Hence such a structure can be considered asa function from attributes to values • Example: • f1(cat)=NP • f1(number)=sg • f1(person)=3 • Values can be atomic or complex: cat NP number singular person third agreement

  30. Subsumption

  31. Subsumption

  32. Subsumption cat NP

  33. Subsumption cat NP cat NP agreement number singular

  34. Subsumption cat NP cat NP agreement number singular cat NP number singular person third agreement

  35. Subsumption cat NP number singular person third agreement cat NP number singular person third subject cat NP agreement number singular cat NP number singular person third agreement

  36. 1 1 Subsumption cat NP number singular person third agreement cat NP number singular person third subject cat NP agreement number singular cat NP number singular person third agreement cat NP number singular person third agreement subject

  37. Not subsumption

  38. Not subsumption cat NP 1 agreement number singular

  39. Not subsumption cat NP 1 agreement number singular cat NP 2 agreement person third

  40. Not subsumption cat NP 1 2, 2 1 1 agreement number singular cat NP 2 agreement person third

  41. Not subsumption cat NP 1 2, 2 1 1 agreement number singular cat NP 2 agreement person third cat NP 3 agreement number plural

  42. Not subsumption cat NP 1 2, 2 1 1 3, 3 1 1 agreement number singular cat NP 2 agreement person third cat NP 3 agreement number plural

  43. Not subsumption cat NP 1 2, 2 1 1 3, 3 1 1 agreement number singular cat NP 2 agreement person third cat NP 3 agreement number plural cat NP 4 number singular person third agreement

  44. Not subsumption cat NP 1 2, 2 1 1 3, 3 1 1 4 1 agreement number singular cat NP 2 agreement person third cat NP 3 agreement number plural cat NP 4 number singular person third agreement

  45. Not subsumption cat NP 1 2, 2 1 1 3, 3 1 1 4 2 4 1 agreement number singular cat NP 2 agreement person third cat NP 3 agreement number plural cat NP 4 number singular person third agreement

  46. Not subsumption cat NP 1 2, 2 1 1 3, 3 1 1 4 2 4 1 2 = 4 1 agreement number singular cat NP 2 agreement person third cat NP 3 agreement number plural cat NP 4 number singular person third agreement

  47. Not subsumption cat NP 1 2, 2 1 1 3, 3 1 1 4 2 4 1 2 = 4 1 3 = fail 1 agreement number singular cat NP 2 agreement person third cat NP 3 agreement number plural cat NP 4 number singular person third agreement

  48. Not subsumption cat NP 1 2, 2 1 1 3, 3 1 1 4 2 4 1 2 = 4 1 3 = fail Unification: ab = c if and only if a c and b c and there is no d such that a d and b d and d c 1 agreement number singular cat NP 2 agreement person third cat NP 3 agreement number plural cat NP 4 number singular person third agreement

  49. Unification

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