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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/sentencesem1update-181205063111/75/Sentence-sem1update-185-2048.jpg)
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Sentence sem1update
- 1.
- 2.
- 3. Boredom • Classes • Meetings •No problems • Playing computer games • Free time
- 4. Blue • Sky • Sea •Music • Soccer team shirt
- 5. Bear • Forest • Zoo •Mountains • Hair
- 6. Bad • Politicians • Globalwarming • Examinations • Stress
- 7. Every • Same asall together? • Same as each? • Both meanings?
- 8. Sentence semantics •X Y •Logic •Mathematical formulae!!
- 9. Sentence semantics •X Y •Logic •Meaning is like computer code??
- 10. Sentence semantics •X Y •If X, then Y
- 11. If X thenY • If you phone me, I will speak to you • If you study hard, you will pass the test • If I get up early, I will be able to go to the zoo • If you put the air conditoner on, it will get cooler • If you give me money, I will be happy
- 12. If X ->Y • If you phone me, I will speak to you • If you study hard, you will pass the test • If I get up early, I will be able to go to the zoo • If you put the air conditoner on, it will get cooler • If you give me money, I will be happy
- 13. If X ->Y • If you study hard, then you will pass the test • X = Bob is a student • Y = Mary bought the book • If Bob is a student, Mary bought the book • ???? • There doesn’t have to be a logical connection • You can say anything
- 14. Sentence semantics •X &Y Z •If X and Y, •then Z
- 15. If X &Y, then Z • If you buy me the ticket and I have free time, I will go to the theater with you • If we win and they lose, I will laugh at them • If a bear comes in the classroom and I have a gun, I will shoot it • If I get the job and the job is well-paid, I will be happy • If you drink the beer and you drink the whisky, you will feel bad
- 16. If X &Y Z • If you buy me the ticket and I have free time, I will go to the theater with you • If we win and they lose, I will laugh at them • If a bear comes in the classroom and I have a gun, I will shoot it • If I get the job and the job is well-paid, I will be happy • If you drink the beer and you drink the whisky, you will feel bad
- 17. If X &Y Z • If Pochi is a dog and you finished your homework, then sushi is delicious. • X = Pochi is a dog • Y = you finished your homework • Z = sushi is delicious • ?????
- 18. If (X &Y) Z • If Pochi is a dog and you finished your homework, then sushi is delicious. • X = Pochi is a dog • Y = you finished your homework • Z = sushi is delicious • ?????
- 19. Why do this? •Seems completely pointless • Maybe it is!
- 20. Propositional Logic • Crazyname • Crazy idea • It’s actually very simple • So don’t worry about it • Just going to have a quick tour
- 21. LOGIC • Very importantin Computer Science
- 22. Words have amazingpower
- 24.
- 25.
- 26.
- 28. And don’t forget… we don’t know where meaning comes from!
- 29. So there’s aproblem for Semantics • We don’t know where meaning comes from • And meaning in words is incredibly complicated • So just thinking about words, we get lost
- 30.
- 31. Full of information,concepts, meaning
- 32. That we cannotreally explain
- 33.
- 34. Sometimes just wordis OK
- 35. But usually wespeak in sentences
- 36. • And sometimessentences are very long, and keep going on and on without giving very much useful information and you start to lose interest and ……
- 37.
- 38. … contain hugeamounts of information
- 39.
- 40.
- 41.
- 42. I saw abrown bear • Who is “I”? • Let’s say “I” is an individual called Jim • What does the meaning of “Jim” look like in your mind? • What does “see” look like in your mind? • etc
- 43. Lots of thingswe cannot explain …
- 44. Really … notat all
- 45. So how dowe begin to understand? • First step • Simplify • Simplify a lot • So it sometimes seems stupid • And very very very very • Very • Boring
- 46.
- 47.
- 48.
- 49.
- 50. Don’t forget …it’s a mystery
- 51.
- 52.
- 53. • Any sentence= p • Or = q • Or = some other letter, like r for example • It’s not really important
- 54. Propositional logic: atomicstatements
- 55. • Truth values •p = 1 • Means: p is true
- 56. • Truth values •p = 0 • Means: p is false
- 57. • p =T • p = F • That is also OK • It’s not really important
- 58. • The importantthing is … • … talking about TRUTH values. • It’s a theory about true and false. • Any problem with that? • No? • OK. • Prepare to be bored!
- 59. Propositional logic: nostructure at all • p = a grizzly is a bear • q = a bear is a mammal • r = a grizzly is a mammal • If p is true • And q is true • Then r is true • p & q r
- 60. Sentences have NOstructure! • p = some sentence or other • q = some other sentence or other • r = some other, different, sentence or other • And so on • Notice they’re supposed to be lower-case letters
- 61. • Let’s lookat an example of this • A very simple example
- 62. • p (somesentence) • r (some sentence) • (if … then connective) • p r • What does this mean? • If p is true, then r is also true
- 63. • If youare human, then you are a mammal • If … then connective
- 64. • p r • p = you are human • r = you are a mammal • If p is true • Then r is also true
- 65. • p &q r • p = you are Japanese • q = You go to university • r = you can write Kanji • That’s a commonsense example • But it doesn’t HAVE to be commonsense
- 66. • We canhave crazy examples if we want
- 67. • p &q r • If p is true and q is true, then r is true • p = a salmon is a fish • q = a fish is human • r = a salmon is human • p is true • q is false • r is false
- 68. • p &q r • What does this mean? • Three sentences p, q, r • It means … • If p and q are both true, • Then r is also true
- 69. Propositions • A fishis human • My teachers are turtles • John’s friend is flying • Her camera is transparent • The Little Prince is standing
- 70. Propositions • Try tokeep it simple • Passives are treated as the same as the active form • John kicked the ball = the ball was kicked by John
- 71. Propositions • John hitBen • Ben was hit by John • Same proposition • call it p • or q • or r • etc
- 72. p = Benis studying
- 73. p: Ben isstudying • Ben is studying = True • p = True • p = T • p = 1
- 74. p = Benis studying
- 75. p: Ben isstudying • Ben is studying = False • p = False • p = F • p = 0
- 76. But maybe he’sstudying?!
- 77. Maybe, but don’tworry too much
- 78.
- 79. Imagine simple littleworlds
- 80. Where everything iseither T or F
- 81. p = TheLittle Prince is standing (= T)
- 82. q = TheLittle Prince is gardening (=T)
- 83. r = TheLittle Prince is Playing soccer (= F)
- 84. Quiz • If yousleep in class then you will not understand the lesson • X Y • X = you sleep in class • Y = you will fail the test
- 85. • If youdrop the glass, then it will break • X Y • X = you drop the glass • Y = it will break
- 86. • If youeat too much, you will gain weight • X Y • X = you eat too much • Y = you will gain weight
- 87. • If youthrow your money out of the window, the teacher will get angry • X Y • X = you throw your money out of the window • Y = the teacher will get angry
- 88. • X &Y Z • If you sleep in class and I see you, then I will get angry • X = you sleep in class • Y = I see you • Z = I will get angry
- 89. • X &Y Z • If we go to the zoo and we bring food, then we can have a picnic • X = we go to the zoo • Y = we bring food • Z = we can have a picnic
- 90. • X &Y Z • If I do a part time job and I don’t spend much, I can save some money • X = I do a part time job • Y = I don’t spend much • Z = I can save some money
- 91. • X &Y Z • If I exercise a lot and I eat less, I will be very fit • X = I exercise a lot • Y = I eat less • Z = I will be very fit
- 93. Logical Constants orconnectives • ∧ • & • And • ∨ • Or • → • If … then
- 94. Connectives • ¬ • Not •~ • Not • - • Not
- 95. Connectives ⇒ → If… then p →q p = you are clever q = you will study If you are clever, you will study
- 96. Connectives ⇒ → If… then p →q p = you are clever q = you will pass the test If you are clever, you will pass the test
- 97. Connectives ⇒ → If… then p →q p = you are studying logic q = you are bored If you are studying logic, you are bored
- 98. Connectives ⇒ → If… then p →q p = you are studying logic q = you hate your teacher If you are studying logic, you hate your teacher
- 99. Connectives ⇒ → If… then p →q p = Eri hates logic q = Eri studies logic If Eri hates logic then she studies logic
- 100. Connectives • ≡ • ⇔ • • equivalence • if and only if (iff) • p = Jim is a man • q = Jim is an adult male human • p≡q • p⇔q
- 101. Equivalence • p =Ken and Emi are married • q = Ken and Emi have a certificate showing they got married • p≡q • p⇔q
- 102. p & q •p = The weather is fine • q = Tom is sleeping • Is p & q true? • If both p & q it is true • Not otherwise
- 103.
- 104. • P vQ • P or Q • - P • Not P
- 105. • If weknow P or Q is true • And we know P is not true • Then Q must be true • Reasoning
- 106. Propositional Logic –too simple • p • q • No internal structure
- 107. John likes Mary •p = John likes Mary • p • What happened to John and Mary? • And what happened to the verb? • What happened to the meaning?
- 108. • John likesMary • Likes (x, y) • x = John • y = Mary
- 109. • John likesMary • Likes (j, m) • j = John • m = Mary
- 110. • Ken gaveEmi the book • Gave (x, y, z) • X = ken • Y = Emi • Z = the book
- 111. • Ken gaveEmi the book • Gave (k, e, b)
- 112.
- 113.
- 114. Predicate Logic • Abit like computer code
- 115.
- 116. Predicate Logic • Predicate •For example … • Love • Love (x,y)
- 117. Predicate • Love • Twoarguments • Love (x, y) • x = john • x = mary • Love (john, mary)
- 118. Predicate • Ken iscrazy • What’s the predicate? • Crazy • How many arguments? • One • What is it? • Ken
- 119. Ken is crazy •Predicate • Crazy • One argument • Crazy (x) • x = ? • x = ken • Crazy (ken)
- 120. Ken walks • Walks( ) • Walks (x) • X = ken • Walks (k)
- 121. What’s the pointof this? • Well information is entered into computers like this all the time • It’s boring? • Don’t blame me
- 122. Love • Two-place predicate •John loves Mary • Loves (john, mary)
- 123. Crazy • One-place predicate •Ken is crazy • Crazy (ken)
- 124. How about three-placepredicate? • Send • Ken sent Mary a letter • Send (ken, mary, letter)
- 125. Predicate is capital •Love (x,y)
- 126. Arguments are smallletters • Love (john, mary) • Why? • Why not? • Who cares?
- 127. Japan is acountry
- 128. Japan is acountry • Country (x) • x = japan • Country (japan)
- 129. Easy so far? •Yes • But what is the point? • Good question
- 130. It helps withcomputer programming
- 131. Peter fell over •Predicate? • Fell_over • How many arguments? • One – peter • Fell_over (peter)
- 132. 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
- 133. Ben hates computers •Hate (ben, computers)
- 134. Eri gave up •Gave_up (eri)
- 135. Eri is agenius • Genius (eri)
- 136. Hit • Hit () • Hit (x, ) • Hit (x, y) • X = bill • Y = ken • Bill hit Ken
- 137.
- 138. The Little Princeis wearing a brown scarf
- 139. • Wearing_a_brown_scarf (p) •Wearing (p, b_s)
- 140. But the LittlePrince is the only person in this world
- 141. Everyone is wearinga brown scarf
- 142. Imagine simple littleworlds
- 143. What do quantifiersmean?
- 144.
- 145.
- 146. • Two sets •Set A • Set B
- 147. • Set A= the set of Linguists • Linguist (x) • Set B = the set of crazy people • Crazy_person (x)
- 148. Who is inthese sets? • Linguist (x) • {evans, • imai, • ono}
- 149. • Linguist (evans) •Linguist (imai) • Linguist (ono) • Set of linguists = • {evans, imai, ono}
- 150. Who is inthe set of crazy people? • Crazy_person (x) • {ken, • jim, • ben, • mary, • evans}
- 151. • Crazy_person (evans) •Crazy_person (ken) • Crazy_person (jim) • Crazy_person (ben) • Crazy_person (mary)
- 152. 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.
- 153. • Set A= the set of Linguists • Linguist (x) • Set B = the set of crazy people • Crazy_person (x)
- 154. Who is inthese sets? • Linguist (x) • {evans, • imai, • ono}
- 155. Who is inthe set of crazy people? • Crazy_person (x) • {ken, • jim, • ben, • mary, • evans}
- 156. 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.
- 157. Some linguists arecrazy • Is this True?
- 158. 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
- 159. Who is inthe set of crazy people? • Crazy_person (x) • {ken, • jim, • ben, • mary, • evans}
- 160. 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
- 161. Predicate • Mary isa girl • Girl • Girl (mary)
- 162. Predicate • Mary livesin Tsuru • Lives_in_Tsuru (mary)
- 163. Set of girls •Girl (mary) • Girl (eri) • Girl (rie) • Girl = {mary, eri, rie}
- 164. Set of peoplewho live in Tsuru • Live_in_tsuru (ben) • Live_in_tsuru (ken) • Live_in_tsuru (mary) • Live in Tsuru = {ben, ken, mary}
- 165. A girl livesin Tsuru • ∃x • ( • Girl (x) • & Lives_in_tsuru (x) • ) • ∃x (Girl (x) & Lives_in_tsuru (x))
- 166. Set of girls •Girl (mary) • Girl (eri) • Girl (rie) • Girl = {mary, eri, rie}
- 167. Set of peoplewho live in Tsuru • Live_in_tsuru (ben) • Live_in_tsuru (ken) • Live_in_tsuru (mary) • Live in Tsuru = {ben, ken, mary}
- 168. • ∃x (Girl(x) & Lives_in_tsuru (x)) • Is True!
- 169. A girl livesin Fujiyoshida • ∃x • ( • Girl (x) • & Lives_in_fujiyoshida (x) • ) • ∃x (Girl (x) & Lives_in_fujiyoshida (x))
- 170. Set of girls •Girl (mary) • Girl (eri) • Girl (rie) • Girl = {mary, eri, rie}
- 171. Set of peoplewho live in Fujiyoshida • Live_in_tsuru (ben) • Live_in_tsuru (len) • Live_in_tsuru (stan) • Live in Tsuru = {ben, len, stan}
- 172. • ∃x (Girl(x) & Lives_in_fujiyoshida (x)) • Is False!
- 173. • 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
- 174. Any problems withPredicate Logic? • Yes • We are not always trying to say things that are true
- 175. The sky isblue
- 176. We don’t saythe sky is blue at night
- 177. Even though it’strue
- 178. • 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))
- 179. • 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?
- 180. New ideas abouthow we understand meaning
- 181. Strong evidence forIMAGES rather than CODE
- 182. Strong evidence forACTION simulation
- 183. Mental Models asIMAGES
- 184. Many people sayLogical Form cannot be real
- 185. 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)
- 186. • ∀x (Child(x) Kissed (nurse, x)) on x’s birthday • The nurse kissed every child on his birthday
- 187. But Logic isVERY important in Linguistics
- 188. p → q •p = Jim is dead • q = Mary is sad • p → q = If Jim is dead, Mary is sad
- 189. p V q •p = My parrot is clever • q = Taro fell over • p V q = (either) my parrot is clever or Taro fell over
- 190. p → q •p = I study hard • q = I will pass the test • p → q = If I study hard, I will pass the test
- 191. ¬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)
- 192. p → q •Normal everyday values for p and q • p = a bear has warm blood • q = a bear is a mammal
- 193. ¬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
- 194. ∃x(G(x) & F(x)) •G = Girl • F = Lives in Fujiyoshida • ∃x(G(x) & F(x)) • A girl lives in Fujiyoshida
- 195. ∀ x(S(x) →C(x)) • S = Student • C = Cried • ∀ x(S(x) → C(x)) • Every student cried
- 196. ∃x(P(x) & R(x)) •Normal everyday sense • P = Professor • R = runs to work • ∃x(P(x) & R(x)) • A professor runs to work
- 197. ∀ x(J(x) →K(x)) • Normal everyday sense • J = car • K = crashed • ∀ x(J(x) → K(x)) • Every car crashed
- 198. 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?