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![But Logic is VERY important in
Linguistics!
• The nurse kissed every child on his birthday.
• [The nurse] kissed [every child] on his birthday.
• Kissed (nurse, every_child)](https://image.slidesharecdn.com/predicatecalculus-181213051207/85/Predicate-calculus-69-320.jpg)
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More from Hywel Evans
Predicate calculus
- 1. Propositional Logic • p q • NO internal structure
- 2. Predicate logic • Loves(j, m) • DOES have internal structure
- 3. Japan is acountry
- 4. Japan is acountry • Country (x) • x = japan • Country (japan)
- 5. Easy so far? •Yes • But what is the point? • Good question
- 6. It helps withcomputer programming
- 7. We use itto input data
- 8.
- 9. Data • You canput in any information you want
- 10. Peter fell over •Predicate? • Fell_over • How many arguments? • One – peter • Fell_over (peter)
- 11. Jim donated $100to the city hospital • Donated (x,…..n) • Donated (jim, $100, city_hospital) • Donated (x, y, z) • X = Jim • Y = $100 • Z= the city hospital
- 12. Ben hates computers •Hate (ben, computers)
- 13. Eri gave up •Gave_up (eri)
- 14. Emi is agenius • Genius (emi)
- 15. No limits aslong as it’s organized • Visit (mary, familiymart, sat_15th_april,) • Computational Linguistics: • Verb • Subject • Complement
- 16. Hit • Hit () • Hit (x, ) • Hit (x, y) • X = bill • Y = ken • Bill hit Ken
- 17.
- 18. The Little Princeis wearing a brown scarf
- 19. • Wearing_a_brown_scarf (p) •Wearing (p, b_s)
- 20. But the LittlePrince is the only person in this world
- 21. Everyone is wearinga brown scarf
- 22. Imagine simple littleworlds
- 23. What do quantifiersmean?
- 24.
- 25.
- 26. • Two sets •Set A • Set B
- 27. • Set A= the set of Linguists • Linguist (x) • Set B = the set of crazy people • Crazy_person (x)
- 28. Who is inthese sets? • Linguist (x) • {evans, • imai, • ono}
- 29. Computer database • Linguist(evans) • Linguist (imai) • Linguist (ono) • Set of linguists = • {evans, imai, ono}
- 30. Who is inthe set of crazy people? • Crazy_person (x) • {ken, • jim, • ben, • mary, • evans}
- 31. Computer database • Crazy_person(evans) • Crazy_person (ken) • Crazy_person (jim) • Crazy_person (ben) • Crazy_person (mary)
- 32. Linguist (x) Crazy_person (x)
- 33. All linguists arecrazy • ∀x (Linguist (x) Crazy_person (x)) • Is this true? • For all individuals x, if x is in the set of Linguists, x is also in the set of Crazy persons.
- 34. • Set A= the set of Linguists • Linguist (x) • Set B = the set of crazy people • Crazy_person (x)
- 35. Who is inthese sets? • Linguist (x) • {evans, • imai, • ono}
- 36. Who is inthe set of crazy people? • Crazy_person (x) • {ken, • jim, • ben, • mary, • evans}
- 37. All linguists arecrazy • ∀x (Linguist (x) Crazy_person (x)) • Is Untrue • Because two members of the set of linguists are not in the set of crazy people.
- 38. Some linguists arecrazy • Is this True?
- 39. • Linguist (x)& Crazy_person (x)
- 40. Some linguists arecrazy • ∃x (Linguist (x) & Crazy_person (x)) • Backward E • Existential Quantifier • There is at least one individual x • x is a linguist • And x is crazy
- 41. Who is inthe set of crazy people? • Crazy_person (x) • {ken, • jim, • ben, • mary, • evans}
- 42. Evans is inthe set of crazy people • So this is true • ∃x (Linguist (x) & Crazy_person (x)) • Backward E • Existential Quantifier • There is at least one individual x • x is a linguist • And x is crazy
- 43. Predicate • Mary isa girl • Girl • Girl (mary)
- 44. Predicate • Mary livesin Tsuru • Lives_in_Tsuru (mary)
- 45. Set of girls •Girl (mary) • Girl (eri) • Girl (rie) • Girl = {mary, eri, rie}
- 46. Set of peoplewho live in Tsuru • Live_in_tsuru (ben) • Live_in_tsuru (ken) • Live_in_tsuru (mary) • Live in Tsuru = {ben, ken, mary}
- 47. A girl livesin Tsuru • ∃x • ( • Girl (x) • & Lives_in_tsuru (x) • ) • ∃x (Girl (x) & Lives_in_tsuru (x))
- 48. Set of girls •Girl (mary) • Girl (eri) • Girl (rie) • Girl = {mary, eri, rie}
- 49. Set of peoplewho live in Tsuru • Live_in_tsuru (ben) • Live_in_tsuru (ken) • Live_in_tsuru (mary) • Live in Tsuru = {ben, ken, mary}
- 50. • ∃x (Girl(x) & Lives_in_tsuru (x)) • Is True!
- 51. A girl livesin Fujiyoshida • ∃x • ( • Girl (x) • & Lives_in_fujiyoshida (x) • ) • ∃x (Girl (x) & Lives_in_fujiyoshida (x))
- 52. Set of girls •Girl (mary) • Girl (eri) • Girl (rie) • Girl = {mary, eri, rie}
- 53. Set of peoplewho live in Fujiyoshida • Live_in_tsuru (ben) • Live_in_tsuru (len) • Live_in_tsuru (stan) • Live in Tsuru = {ben, len, stan}
- 54. • ∃x (Girl(x) & Lives_in_fujiyoshida (x)) • Is False!
- 55. • But • ¬∃x(Girl (x) & Lives_in_fujiyoshida (x)) • Is true • ~∃x (Girl (x) & Lives_in_fujiyoshida (x)) • Is true • -∃x (Girl (x) & Lives_in_fujiyoshida (x)) • Is true
- 56. Any problems withPredicate Logic? • Yes • We are not always trying to say things that are true
- 57. The sky isblue
- 58. We don’t saythe sky is blue at night
- 59. Even though it’strue
- 60. • We sometimessay things that are not true • “My brain exploded” • And do we really think in Logical Form? • ¬∃x (Girl (x) & Lives_in_fujiyoshida (x))
- 61. • And ifI say “A girl lives in Fujiyoshida” … • … is it really a statement about existence of an individual? • Or am I more concerned with number • Or the fact that we’re talking about a girl rather than a boy? • Or a girl rather than a woman? • Or something else related to CONTEXT?
- 62. New ideas abouthow we understand meaning
- 63. Language connects tothe body
- 64. NOT all inthe brain!
- 65. Also strong evidencefor IMAGES rather than CODE
- 66. Strong evidence forACTION simulation
- 67. Mental Models asIMAGES
- 68. Many people sayLogical Form cannot be real
- 69. But Logic isVERY important in Linguistics! • The nurse kissed every child on his birthday. • [The nurse] kissed [every child] on his birthday. • Kissed (nurse, every_child)
- 70. • ∀x (Child(x) Kissed (nurse, x)) on x’s birthday • The nurse kissed every child on his birthday
- 71. But Logic isVERY important in Linguistics
- 72. And logic isthe basis of computer science
- 73. ∃ (existential) • M(jen,mary) •M = mother • Jen is Mary’s mother • ∃xM(x,y) • Someone is the mother of y
- 74. • ∀y∃xM(x,y) • Everyonehas a mother
- 75. • Likes (ben,emi) • Ben likes Emi • Likes (x, y) • x likes y
- 76. X = boys,Y = girls • Likes (x, y) • x likes y • (let’s say x = boys and y = girls) • ∃y (Likes (x, y) • There is some girl that x likes
- 77. • ∃y (Likes(x, y) • There is some girl that x likes • ∀x∃y (Likes (x, y) • Each boy likes a girl
- 78. Each boy likesa girl Boys Girls
- 79. ∀x∃y (Likes (x,y) Boys Girls
- 80. There’s one girlall the boys like Boys Girls
- 81. All the boyslike one girl Boys Girls
- 82. ∃y∀x (Likes (x,y) Boys Girls
- 83. p → q •p = Jim is dead • q = Mary is sad • p → q = • If Jim is dead, Mary is sad
- 84. p V q •p = My parrot is clever • q = Taro fell over • p V q = • (either) my parrot is clever or Taro fell over
- 85. p → q •p = I study hard • q = I will pass the test • p → q = • If I study hard, I will pass the test
- 86. ¬p → ¬q •P = I study hard • Q = I will pass the test • ¬p → ¬q = If I do not study hard, I will not pass the test • If NOT(I study hard) then NOT (I will pass the test)
- 87. p → q •Normal everyday values for p and q • p = a bear has warm blood • q = a bear is a mammal
- 88. ¬p → q •Normal everyday values for p and q • p = you study hard • q = you will fail • If you DON’T study hard, you will fail
- 89. Modern Linguistics • Studyinglanguage helps us understand the human brain • Do you think the human brain works like computer code? • Do you think studying language tells us something about the brain?