Semantics and Pragmatics of NLP Lascarides & Klein Ambiguity - PowerPoint PPT Presentation

SPNLP: Ambiguity and Underspecifi- cation Semantics and Pragmatics of NLP Lascarides & Klein Ambiguity and Underspecification Outline Representing Ambiguity Conclusion Alex Lascarides & Ewan Klein School of Informatics University of Edinburgh 31 January 2008

SPNLP: Ambiguity and Underspecifi- cation Lascarides & Klein Outline 1 Representing Ambiguity Representing Ambiguity Conclusion Conclusion 2

Operator Ambiguity SPNLP: Ambiguity and Underspecifi- cation Lascarides & Klein Outline Don’t choose the fish starter or order white wine. Representing Ambiguity 1 ¬ ( choose-fish ∨ order-white-wine ) Conclusion 2 ( ¬ choose-fish ) ∨ order-white-wine

Operator Ambiguity SPNLP: Ambiguity and Underspecifi- cation Lascarides & Klein Outline Don’t choose the fish starter or order white wine. Representing Ambiguity 1 ¬ ( choose-fish ∨ order-white-wine ) Conclusion 2 ( ¬ choose-fish ) ∨ order-white-wine

Operator Ambiguity SPNLP: Ambiguity and Underspecifi- cation Lascarides & Klein Outline Don’t choose the fish starter or order white wine. Representing Ambiguity 1 ¬ ( choose-fish ∨ order-white-wine ) Conclusion 2 ( ¬ choose-fish ) ∨ order-white-wine

Quantifier Scope Ambiguity SPNLP: Ambiguity and Underspecifi- cation Every man loves a woman Lascarides & Klein 1 ∀ x ( man ( x ) → ∃ y ( woman ( y ) ∧ love ( x , y ))) Outline 2 ∃ y ( woman ( y ) ∧ ∀ x ( man ( x ) → love ( x , y ))) Representing Ambiguity Semantic scope ambiguity, but: Conclusion Only one syntactic form in most current grammars To advocate syntactic ambiguity is: ad hoc computationally problematic inadequate with respect to pragmatics

Quantifier Scope Ambiguity SPNLP: Ambiguity and Underspecifi- cation Every man loves a woman Lascarides & Klein 1 ∀ x ( man ( x ) → ∃ y ( woman ( y ) ∧ love ( x , y ))) Outline 2 ∃ y ( woman ( y ) ∧ ∀ x ( man ( x ) → love ( x , y ))) Representing Ambiguity Semantic scope ambiguity, but: Conclusion Only one syntactic form in most current grammars To advocate syntactic ambiguity is: ad hoc computationally problematic inadequate with respect to pragmatics

Quantifier Scope Ambiguity SPNLP: Ambiguity and Underspecifi- cation Every man loves a woman Lascarides & Klein 1 ∀ x ( man ( x ) → ∃ y ( woman ( y ) ∧ love ( x , y ))) Outline 2 ∃ y ( woman ( y ) ∧ ∀ x ( man ( x ) → love ( x , y ))) Representing Ambiguity Semantic scope ambiguity, but: Conclusion Only one syntactic form in most current grammars To advocate syntactic ambiguity is: ad hoc computationally problematic inadequate with respect to pragmatics

Quantifier Scope Ambiguity SPNLP: Ambiguity and Underspecifi- cation Every man loves a woman Lascarides & Klein 1 ∀ x ( man ( x ) → ∃ y ( woman ( y ) ∧ love ( x , y ))) Outline 2 ∃ y ( woman ( y ) ∧ ∀ x ( man ( x ) → love ( x , y ))) Representing Ambiguity Semantic scope ambiguity, but: Conclusion Only one syntactic form in most current grammars To advocate syntactic ambiguity is: ad hoc computationally problematic inadequate with respect to pragmatics

Underspecification SPNLP: Ambiguity and Underspecifi- cation Lascarides & Klein Build a partial description of the LF in the grammar: Outline This is called an underspecified semantic Representing representation or USR. Ambiguity Write an algorithm for working out which FOL formulas Conclusion a USR describes. More than one FOL formula ≈ semantic ambiguity. That is, any FOL formula which satisfies a USR is a possible LF .

Underspecification SPNLP: Ambiguity and Underspecifi- cation Lascarides & Klein Build a partial description of the LF in the grammar: Outline This is called an underspecified semantic Representing representation or USR. Ambiguity Write an algorithm for working out which FOL formulas Conclusion a USR describes. More than one FOL formula ≈ semantic ambiguity. That is, any FOL formula which satisfies a USR is a possible LF .

Underspecification SPNLP: Ambiguity and Underspecifi- cation Lascarides & Klein Build a partial description of the LF in the grammar: Outline This is called an underspecified semantic Representing representation or USR. Ambiguity Write an algorithm for working out which FOL formulas Conclusion a USR describes. More than one FOL formula ≈ semantic ambiguity. That is, any FOL formula which satisfies a USR is a possible LF .

Underspecification SPNLP: Ambiguity and Underspecifi- cation Lascarides & Klein Build a partial description of the LF in the grammar: Outline This is called an underspecified semantic Representing representation or USR. Ambiguity Write an algorithm for working out which FOL formulas Conclusion a USR describes. More than one FOL formula ≈ semantic ambiguity. That is, any FOL formula which satisfies a USR is a possible LF .

Underspecification SPNLP: Ambiguity and Underspecifi- cation Lascarides & Klein Build a partial description of the LF in the grammar: Outline This is called an underspecified semantic Representing representation or USR. Ambiguity Write an algorithm for working out which FOL formulas Conclusion a USR describes. More than one FOL formula ≈ semantic ambiguity. That is, any FOL formula which satisfies a USR is a possible LF .

Back to the fish and wine example, 1 SPNLP: Ambiguity and Underspecifi- cation Lascarides & The two readings again: Klein Outline 1 ¬ ( F ∨ W ) Representing Ambiguity 2 ( ¬ F ) ∨ W ) Conclusion Use h i as a variable over sub-formulas: h 1 ∨ W ¬ h 2

Back to the fish and wine example, 2 SPNLP: Ambiguity and Underspecifi- Use h i as a variable over sub-formulas: cation Lascarides & Klein h 1 ∨ W Outline ¬ h 2 Representing Ambiguity Think of h i as a ‘hole’ in the formula. Possible solutions: Conclusion 1 (i) h 1 = F (ii) h 2 = ( F ∨ W ) 2 (i) h 1 = ( ¬ F ) (ii) h 2 = F

Back to the fish and wine example, 2 SPNLP: Ambiguity and Underspecifi- Use h i as a variable over sub-formulas: cation Lascarides & Klein h 1 ∨ W Outline ¬ h 2 Representing Ambiguity Think of h i as a ‘hole’ in the formula. Possible solutions: Conclusion 1 (i) h 1 = F (ii) h 2 = ( F ∨ W ) 2 (i) h 1 = ( ¬ F ) (ii) h 2 = F

Back to the fish and wine example, 2 SPNLP: Ambiguity and Underspecifi- Use h i as a variable over sub-formulas: cation Lascarides & Klein h 1 ∨ W Outline ¬ h 2 Representing Ambiguity Think of h i as a ‘hole’ in the formula. Possible solutions: Conclusion 1 (i) h 1 = F (ii) h 2 = ( F ∨ W ) 2 (i) h 1 = ( ¬ F ) (ii) h 2 = F

Labels and Holes SPNLP: Ambiguity and Use l i as a label over sub-formulas: Underspecifi- cation Lascarides & l 1 : ¬ h 2 Klein l 2 : h 1 ∨ W Outline l 3 : F Representing Ambiguity Conclusion Possible solutions: 1 (i) h 1 = l 3 (ii) h 2 = l 2 2 (i) h 1 = l 1 (ii) h 2 = l 3

Graphical Representation of Solutions SPNLP: h0 h0 Ambiguity and Underspecifi- cation Lascarides & Klein l1: ¬h1 l2: h2 v W Outline Representing Ambiguity Conclusion l2: h2 v W l1: ¬h1 l3: F l3: F NB h 0 represents ‘widest scope’.

Formulas as Trees SPNLP: Ambiguity and ¬ v Underspecifi- cation Lascarides & Klein Outline v ¬ W Representing Ambiguity Conclusion F W F Mother semantically has scope over daughters Left to right order ≈ order of arguments to mother ‘constructor’.

Formulas as Trees SPNLP: Ambiguity and ¬ v Underspecifi- cation Lascarides & Klein Outline v ¬ W Representing Ambiguity Conclusion F W F Mother semantically has scope over daughters Left to right order ≈ order of arguments to mother ‘constructor’.

The Strategy SPNLP: Ambiguity and Underspecifi- cation Lascarides & Design a language which can describe these FOL trees. Klein Introduce labels to refer to nodes of the tree. Outline Representing To simplify matters, only label nodes which are roots for Ambiguity FOL formulas, e.g., Conclusion the nodes that label ∨ , ¬ , etc. Can express information about: what formula a node labels; which node dominates which other nodes (information about relative semantic scope)

The Same Trees with the Labels SPNLP: Ambiguity and Underspecifi- cation Lascarides & l1: ¬ l2: v Klein Outline Representing Ambiguity l2: v l1: ¬ l4: W Conclusion l3: F l4: W l3: F

Dominance Constraints SPNLP: Ambiguity and Underspecifi- cation Lascarides & Klein Partial order ≤ between holes and labels. Outline l i ≤ h j : h j has scope over l i . Representing Ambiguity Note that ≤ is transitive. Conclusion l 3 ≤ h 1 : choose fish (F) is in the scope of don’t ( ¬ ). l 3 ≤ h 2 : choose fish (F) is in the scope of or ( ∨ ). l 1 ≤ h 0 : don’t can take widest scope. l 2 ≤ h 0 : or can take widest scope.

Dominance Constraints SPNLP: Ambiguity and Underspecifi- cation Lascarides & Klein Partial order ≤ between holes and labels. Outline l i ≤ h j : h j has scope over l i . Representing Ambiguity Note that ≤ is transitive. Conclusion l 3 ≤ h 1 : choose fish (F) is in the scope of don’t ( ¬ ). l 3 ≤ h 2 : choose fish (F) is in the scope of or ( ∨ ). l 1 ≤ h 0 : don’t can take widest scope. l 2 ≤ h 0 : or can take widest scope.