SPNLP: From Syntax to Model Checking Semantics and Pragmatics of NLP Lascarides & Klein From Syntax to Model Checking Outline Review Computational Framework Alex Lascarides & Ewan Klein Alternative Input Formats for Valuations Getting the School of Informatics Output University of Edinburgh Summary 10 January 2008
SPNLP: From Syntax to Model Review Checking 1 Lascarides & Klein Computational Framework 2 Outline Review Computational Framework Alternative Input Formats for Valuations 3 Alternative Input Formats for Valuations Getting the Output Getting the 4 Output Summary Summary 5
Logical Syntax and Semantics SPNLP: From Syntax to Model Checking A logical language based on: Lascarides & 1 function-argument structures: ( M N ) Klein 2 lambda abstraction: λ x . ( α x ) Outline 3 beta-reduction: ( λ x . ( M x ) N ) ≡ ( M N ) Review 4 Boolean combinations: ( φ ∧ ψ ) , . . . Computational 5 Quantified formulas: ∀ x .φ , ∃ x .φ Framework Alternative Input Formats for Valuations Models for the language: Getting the 1 M = � D , V � Output 2 variable assignment g : Var �→ D Summary ] M , g for expressions α . 3 recursive definition of [ [ α ] ] M , g ′ = 1. 4 M , g | = φ iff [ [ φ ]
Logical Syntax and Semantics SPNLP: From Syntax to Model Checking A logical language based on: Lascarides & 1 function-argument structures: ( M N ) Klein 2 lambda abstraction: λ x . ( α x ) Outline 3 beta-reduction: ( λ x . ( M x ) N ) ≡ ( M N ) Review 4 Boolean combinations: ( φ ∧ ψ ) , . . . Computational 5 Quantified formulas: ∀ x .φ , ∃ x .φ Framework Alternative Input Formats for Valuations Models for the language: Getting the 1 M = � D , V � Output 2 variable assignment g : Var �→ D Summary ] M , g for expressions α . 3 recursive definition of [ [ α ] ] M , g ′ = 1. 4 M , g | = φ iff [ [ φ ]
Logical Syntax and Semantics SPNLP: From Syntax to Model Checking A logical language based on: Lascarides & 1 function-argument structures: ( M N ) Klein 2 lambda abstraction: λ x . ( α x ) Outline 3 beta-reduction: ( λ x . ( M x ) N ) ≡ ( M N ) Review 4 Boolean combinations: ( φ ∧ ψ ) , . . . Computational 5 Quantified formulas: ∀ x .φ , ∃ x .φ Framework Alternative Input Formats for Valuations Models for the language: Getting the 1 M = � D , V � Output 2 variable assignment g : Var �→ D Summary ] M , g for expressions α . 3 recursive definition of [ [ α ] ] M , g ′ = 1. 4 M , g | = φ iff [ [ φ ]
Logical Syntax and Semantics SPNLP: From Syntax to Model Checking A logical language based on: Lascarides & 1 function-argument structures: ( M N ) Klein 2 lambda abstraction: λ x . ( α x ) Outline 3 beta-reduction: ( λ x . ( M x ) N ) ≡ ( M N ) Review 4 Boolean combinations: ( φ ∧ ψ ) , . . . Computational 5 Quantified formulas: ∀ x .φ , ∃ x .φ Framework Alternative Input Formats for Valuations Models for the language: Getting the 1 M = � D , V � Output 2 variable assignment g : Var �→ D Summary ] M , g for expressions α . 3 recursive definition of [ [ α ] ] M , g ′ = 1. 4 M , g | = φ iff [ [ φ ]
Logical Syntax and Semantics SPNLP: From Syntax to Model Checking A logical language based on: Lascarides & 1 function-argument structures: ( M N ) Klein 2 lambda abstraction: λ x . ( α x ) Outline 3 beta-reduction: ( λ x . ( M x ) N ) ≡ ( M N ) Review 4 Boolean combinations: ( φ ∧ ψ ) , . . . Computational 5 Quantified formulas: ∀ x .φ , ∃ x .φ Framework Alternative Input Formats for Valuations Models for the language: Getting the 1 M = � D , V � Output 2 variable assignment g : Var �→ D Summary ] M , g for expressions α . 3 recursive definition of [ [ α ] ] M , g ′ = 1. 4 M , g | = φ iff [ [ φ ]
Logical Syntax and Semantics SPNLP: From Syntax to Model Checking A logical language based on: Lascarides & 1 function-argument structures: ( M N ) Klein 2 lambda abstraction: λ x . ( α x ) Outline 3 beta-reduction: ( λ x . ( M x ) N ) ≡ ( M N ) Review 4 Boolean combinations: ( φ ∧ ψ ) , . . . Computational 5 Quantified formulas: ∀ x .φ , ∃ x .φ Framework Alternative Input Formats for Valuations Models for the language: Getting the 1 M = � D , V � Output 2 variable assignment g : Var �→ D Summary ] M , g for expressions α . 3 recursive definition of [ [ α ] ] M , g ′ = 1. 4 M , g | = φ iff [ [ φ ]
Logical Syntax and Semantics SPNLP: From Syntax to Model Checking A logical language based on: Lascarides & 1 function-argument structures: ( M N ) Klein 2 lambda abstraction: λ x . ( α x ) Outline 3 beta-reduction: ( λ x . ( M x ) N ) ≡ ( M N ) Review 4 Boolean combinations: ( φ ∧ ψ ) , . . . Computational 5 Quantified formulas: ∀ x .φ , ∃ x .φ Framework Alternative Input Formats for Valuations Models for the language: Getting the 1 M = � D , V � Output 2 variable assignment g : Var �→ D Summary ] M , g for expressions α . 3 recursive definition of [ [ α ] ] M , g ′ = 1. 4 M , g | = φ iff [ [ φ ]
Logical Syntax and Semantics SPNLP: From Syntax to Model Checking A logical language based on: Lascarides & 1 function-argument structures: ( M N ) Klein 2 lambda abstraction: λ x . ( α x ) Outline 3 beta-reduction: ( λ x . ( M x ) N ) ≡ ( M N ) Review 4 Boolean combinations: ( φ ∧ ψ ) , . . . Computational 5 Quantified formulas: ∀ x .φ , ∃ x .φ Framework Alternative Input Formats for Valuations Models for the language: Getting the 1 M = � D , V � Output 2 variable assignment g : Var �→ D Summary ] M , g for expressions α . 3 recursive definition of [ [ α ] ] M , g ′ = 1. 4 M , g | = φ iff [ [ φ ]
Logical Syntax and Semantics SPNLP: From Syntax to Model Checking A logical language based on: Lascarides & 1 function-argument structures: ( M N ) Klein 2 lambda abstraction: λ x . ( α x ) Outline 3 beta-reduction: ( λ x . ( M x ) N ) ≡ ( M N ) Review 4 Boolean combinations: ( φ ∧ ψ ) , . . . Computational 5 Quantified formulas: ∀ x .φ , ∃ x .φ Framework Alternative Input Formats for Valuations Models for the language: Getting the 1 M = � D , V � Output 2 variable assignment g : Var �→ D Summary ] M , g for expressions α . 3 recursive definition of [ [ α ] ] M , g ′ = 1. 4 M , g | = φ iff [ [ φ ]
Logical Syntax and Semantics SPNLP: From Syntax to Model Checking A logical language based on: Lascarides & 1 function-argument structures: ( M N ) Klein 2 lambda abstraction: λ x . ( α x ) Outline 3 beta-reduction: ( λ x . ( M x ) N ) ≡ ( M N ) Review 4 Boolean combinations: ( φ ∧ ψ ) , . . . Computational 5 Quantified formulas: ∀ x .φ , ∃ x .φ Framework Alternative Input Formats for Valuations Models for the language: Getting the 1 M = � D , V � Output 2 variable assignment g : Var �→ D Summary ] M , g for expressions α . 3 recursive definition of [ [ α ] ] M , g ′ = 1. 4 M , g | = φ iff [ [ φ ]
Logical Syntax and Semantics SPNLP: From Syntax to Model Checking A logical language based on: Lascarides & 1 function-argument structures: ( M N ) Klein 2 lambda abstraction: λ x . ( α x ) Outline 3 beta-reduction: ( λ x . ( M x ) N ) ≡ ( M N ) Review 4 Boolean combinations: ( φ ∧ ψ ) , . . . Computational 5 Quantified formulas: ∀ x .φ , ∃ x .φ Framework Alternative Input Formats for Valuations Models for the language: Getting the 1 M = � D , V � Output 2 variable assignment g : Var �→ D Summary ] M , g for expressions α . 3 recursive definition of [ [ α ] ] M , g ′ = 1. 4 M , g | = φ iff [ [ φ ]
Compositional Semantics SPNLP: From Compositionality The meaning of a complex expression is a Syntax to Model function of the meaning of its parts. Checking Lascarides & How do we know what the parts are? Klein Outline Feature-based context-free grammar formalism. Review Every category has a sem feature whose value is the Computational semantics of expressions of that category: Framework lexical categories: fully-instantiated LF. Alternative Input Formats phrasal categories: build an LF by function application for Valuations over the LFs of the daughters. Getting the Output Summary Example PS Rule ❙❬s❡♠ ❂ ❁❛♣♣✭❄s✉❜❥✱❄✈♣✮❃❪ ✲❃ ◆P❬s❡♠❂❄s✉❜❥❪ ❱P❬s❡♠❂❄✈♣❪
Compositional Semantics SPNLP: From Compositionality The meaning of a complex expression is a Syntax to Model function of the meaning of its parts. Checking Lascarides & How do we know what the parts are? Klein Outline Feature-based context-free grammar formalism. Review Every category has a sem feature whose value is the Computational semantics of expressions of that category: Framework lexical categories: fully-instantiated LF. Alternative Input Formats phrasal categories: build an LF by function application for Valuations over the LFs of the daughters. Getting the Output Summary Example PS Rule ❙❬s❡♠ ❂ ❁❛♣♣✭❄s✉❜❥✱❄✈♣✮❃❪ ✲❃ ◆P❬s❡♠❂❄s✉❜❥❪ ❱P❬s❡♠❂❄✈♣❪
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