Computational Semantics L4: Ambiguity and underspecification Simon Dobnik [email protected] April 11, 2019 Outline Ambiguity in natural language The computational problem with ambiguity Underspecification Outline Ambiguity in natural language The computational problem with ambiguity Underspecification I Kim ran to the riverbank. I Kim ran to the bank to get her money. I Kim ran to the bank before it closed. Lexical ambiguity I Kim ran to the bank. 4 / 38 I Kim ran to the bank to get her money. I Kim ran to the bank before it closed. Lexical ambiguity I Kim ran to the bank. I Kim ran to the riverbank. 4 / 38 I Kim ran to the bank before it closed. Lexical ambiguity I Kim ran to the bank. I Kim ran to the riverbank. I Kim ran to the bank to get her money. 4 / 38 Lexical ambiguity I Kim ran to the bank. I Kim ran to the riverbank. I Kim ran to the bank to get her money. I Kim ran to the bank before it closed. 4 / 38 Syntactic ambiguity without semantic ambiguity I NP ! NP and NP I Kim and Lee and Chris arrived early. 5 / 38 S NP VP arrived early NP andNP NP andNP Chris Kim Lee 6 / 38 S NP VP arrived early NP andNP Kim NP andNP Lee Chris 7 / 38 Syntactic ambiguity with semantic ambiguity I NP ! NP or NP I Kim and Lee or Chris arrived early 8 / 38 S NP VP arrived early NP or NP NP andNP Chris Kim Lee True if only Chris arrived early 9 / 38 S NP VP arrived early NP andNP Kim NP orNP Lee Chris False if only Chris arrived early 10 / 38 I Kimi saw Leej and shei smiled at himj I Kimi saw Leej and shej smiled at himi Anaphora I Kim saw Lee and she smiled at him 11 / 38 I Kimi saw Leej and shej smiled at himi Anaphora I Kim saw Lee and she smiled at him I Kimi saw Leej and shei smiled at himj 11 / 38 Anaphora I Kim saw Lee and she smiled at him I Kimi saw Leej and shei smiled at himj I Kimi saw Leej and shej smiled at himi 11 / 38 I two boys ate two pizzas I most students read most books I 9x[company representative(x) ^ 8y[new employee(y) ! interview(x; y)]] I 8y[new employee(y) ! 9x[company representative(x) ^ interview(x; y)]] I some surprising examples: Quantifier scope ambiguity I a company representative interviews every new employee 12 / 38 I two boys ate two pizzas I most students read most books I 8y[new employee(y) ! 9x[company representative(x) ^ interview(x; y)]] I some surprising examples: Quantifier scope ambiguity I a company representative interviews every new employee I 9x[company representative(x) ^ 8y[new employee(y) ! interview(x; y)]] 12 / 38 I two boys ate two pizzas I most students read most books I some surprising examples: Quantifier scope ambiguity I a company representative interviews every new employee I 9x[company representative(x) ^ 8y[new employee(y) ! interview(x; y)]] I 8y[new employee(y) ! 9x[company representative(x) ^ interview(x; y)]] 12 / 38 I two boys ate two pizzas I most students read most books Quantifier scope ambiguity I a company representative interviews every new employee I 9x[company representative(x) ^ 8y[new employee(y) ! interview(x; y)]] I 8y[new employee(y) ! 9x[company representative(x) ^ interview(x; y)]] I some surprising examples: 12 / 38 I most students read most books Quantifier scope ambiguity I a company representative interviews every new employee I 9x[company representative(x) ^ 8y[new employee(y) ! interview(x; y)]] I 8y[new employee(y) ! 9x[company representative(x) ^ interview(x; y)]] I some surprising examples: I two boys ate two pizzas 12 / 38 Quantifier scope ambiguity I a company representative interviews every new employee I 9x[company representative(x) ^ 8y[new employee(y) ! interview(x; y)]] I 8y[new employee(y) ! 9x[company representative(x) ^ interview(x; y)]] I some surprising examples: I two boys ate two pizzas I most students read most books 12 / 38 Evaluating expressions with quantifiers evaluating-quantifiers.ipynb or .py 13 / 38 Outline Ambiguity in natural language The computational problem with ambiguity Underspecification I 5! = 120 readings I . but no politician can fool all of the people all of the time How many readings? I In most democratic countries most politicians can fool most of the people on almost every issue most of the time. (Hobbs, 1983) 15 / 38 I . but no politician can fool all of the people all of the time How many readings? I In most democratic countries most politicians can fool most of the people on almost every issue most of the time. (Hobbs, 1983) I 5! = 120 readings 15 / 38 How many readings? I In most democratic countries most politicians can fool most of the people on almost every issue most of the time. (Hobbs, 1983) I 5! = 120 readings I . but no politician can fool all of the people all of the time 15 / 38 I first you have to explain to the user what the ambiguity is. I . and then it is not clear that you can find enough unambiguous natural language sentences to express the different readings I so the user has to know logic! How do you disambiguate? I not practical to ask users to disambiguate 16 / 38 I . and then it is not clear that you can find enough unambiguous natural language sentences to express the different readings I so the user has to know logic! How do you disambiguate? I not practical to ask users to disambiguate I first you have to explain to the user what the ambiguity is. 16 / 38 I so the user has to know logic! How do you disambiguate? I not practical to ask users to disambiguate I first you have to explain to the user what the ambiguity is. I . and then it is not clear that you can find enough unambiguous natural language sentences to express the different readings 16 / 38 How do you disambiguate? I not practical to ask users to disambiguate I first you have to explain to the user what the ambiguity is. I . and then it is not clear that you can find enough unambiguous natural language sentences to express the different readings I so the user has to know logic! 16 / 38 Outline Ambiguity in natural language The computational problem with ambiguity Underspecification Packing several meanings in a single representation I finding all the readings is computationally inefficient I . and then you have to figure out which of the meanings was meant I Underspecified meaning representations allow you to compute one single representation from which you can generate specified meanings if necessary 18 / 38 Cooper storage (Cooper, 1983) 19 / 38 interview(x1; x0) hλP[9x[rep(x) ^ P(x)]]; 1i hλP[8x[employee(x) ! P(x)]]; 0i λP[P(x1)] λx[interview(x; x0)] hλP[9x[rep(x) ^ P(x)]]; 1i hλP[8x[employee(x) ! P(x)]]; 0i λP[P(x0)] hλP[8x[employee(x) ! P(x)]]; 0i S NP VP a representative interviewsNP every employee interview(x1; x0) hλP[9x[rep(x) ^ P(x)]]; 1i hλP[8x[employee(x) ! P(x)]]; 0i λP[P(x1)] λx[interview(x; x0)] hλP[9x[rep(x) ^ P(x)]]; 1i hλP[8x[employee(x) ! P(x)]]; 0i S NP VP a representative interviewsNP λP[P(x0)] hλP[8x[employee(x) ! P(x)]]; 0i every employee interview(x1; x0) hλP[9x[rep(x) ^ P(x)]]; 1i hλP[8x[employee(x) ! P(x)]]; 0i λP[P(x1)] hλP[9x[rep(x) ^ P(x)]]; 1i S NP VP λx[interview(x; x0)] hλP[8x[employee(x) ! P(x)]]; 0i a representative interviewsNP λP[P(x0)] hλP[8x[employee(x) ! P(x)]]; 0i every employee interview(x1; x0) hλP[9x[rep(x) ^ P(x)]]; 1i hλP[8x[employee(x) ! P(x)]]; 0i S NP VP λP[P(x1)] λx[interview(x; x0)] hλP[9x[rep(x) ^ P(x)]]; 1i hλP[8x[employee(x) ! P(x)]]; 0i a representative interviewsNP λP[P(x0)] hλP[8x[employee(x) ! P(x)]]; 0i every employee S interview(x1; x0) hλP[9x[rep(x) ^ P(x)]]; 1i hλP[8x[employee(x) ! P(x)]]; 0i NP VP λP[P(x1)] λx[interview(x; x0)] hλP[9x[rep(x) ^ P(x)]]; 1i hλP[8x[employee(x) ! P(x)]]; 0i a representative interviewsNP λP[P(x0)] hλP[8x[employee(x) ! P(x)]]; 0i every employee I λP[9x[rep(x) ^ P(x)]](λx1[interview(x1; x0)]) hλP[8x[employee(x) ! P(x)]]; 0i I 9x[rep(x) ^ interview(x; x0)]) hλP[8x[employee(x) ! P(x)]]; 0i I λP[8x[employee(x) ! P(x)]](λx0[9x[rep(x) ^ interview(x; x0)]]) I 8y[employee(y) ! 9x[rep(x) ^ interview(x; y)]] Retrieval I interview(x1; x0) hλP[9x[rep(x) ^ P(x)]]; 1i hλP[8x[employee(x) ! P(x)]]; 0i 21 / 38 I 9x[rep(x) ^ interview(x; x0)]) hλP[8x[employee(x) ! P(x)]]; 0i I λP[8x[employee(x) ! P(x)]](λx0[9x[rep(x) ^ interview(x; x0)]]) I 8y[employee(y) ! 9x[rep(x) ^ interview(x; y)]] Retrieval I interview(x1; x0) hλP[9x[rep(x) ^ P(x)]]; 1i hλP[8x[employee(x) ! P(x)]]; 0i I λP[9x[rep(x) ^ P(x)]](λx1[interview(x1; x0)]) hλP[8x[employee(x) ! P(x)]]; 0i 21 / 38 I λP[8x[employee(x) ! P(x)]](λx0[9x[rep(x) ^ interview(x; x0)]]) I 8y[employee(y) ! 9x[rep(x) ^ interview(x; y)]] Retrieval I interview(x1; x0) hλP[9x[rep(x) ^ P(x)]]; 1i hλP[8x[employee(x) ! P(x)]]; 0i I λP[9x[rep(x) ^ P(x)]](λx1[interview(x1; x0)]) hλP[8x[employee(x) ! P(x)]]; 0i I 9x[rep(x) ^ interview(x; x0)]) hλP[8x[employee(x) ! P(x)]]; 0i 21 / 38 I 8y[employee(y) ! 9x[rep(x) ^ interview(x; y)]] Retrieval I interview(x1; x0) hλP[9x[rep(x) ^ P(x)]]; 1i hλP[8x[employee(x) ! P(x)]]; 0i I λP[9x[rep(x) ^ P(x)]](λx1[interview(x1; x0)]) hλP[8x[employee(x) ! P(x)]]; 0i I 9x[rep(x) ^ interview(x; x0)]) hλP[8x[employee(x) ! P(x)]]; 0i I λP[8x[employee(x) ! P(x)]](λx0[9x[rep(x) ^ interview(x; x0)]]) 21 / 38 Retrieval I interview(x1; x0) hλP[9x[rep(x) ^ P(x)]]; 1i hλP[8x[employee(x) ! P(x)]]; 0i I λP[9x[rep(x) ^ P(x)]](λx1[interview(x1; x0)]) hλP[8x[employee(x) ! P(x)]]; 0i I 9x[rep(x) ^ interview(x; x0)]) hλP[8x[employee(x) ! P(x)]]; 0i I λP[8x[employee(x) ! P(x)]](λx0[9x[rep(x) ^ interview(x; x0)]]) I 8y[employee(y) ! 9x[rep(x) ^ interview(x; y)]] 21 / 38 I λP[8x[employee(x) ! P(x)]](λx0[interview(x1; x0)]) hλP[9x[rep(x) ^ P(x)]]; 1i I 8x[employee(x) ! interview(x1; x)] hλP[9x[rep(x) ^ P(x)]]; 1i I λP[9x[rep(x) ^ P(x)]](λx1[8x[employee(x) ! interview(x1; x)]]) I 9y[rep(y) ^ 8x[employee(x) ! interview(y; x)]] Retrieval, contd.