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

SPNLP: From Syntax to Model Checking Lascarides & Klein Outline Review Computational Framework Alternative Input Formats for Valuations Getting the Output Summary

Semantics and Pragmatics of NLP From Syntax to Model Checking

Alex Lascarides & Ewan Klein

School of Informatics University of Edinburgh

10 January 2008

SPNLP: From Syntax to Model Checking Lascarides & Klein Outline Review Computational Framework Alternative Input Formats for Valuations Getting the Output Summary

1

Review

2

Computational Framework

3

Alternative Input Formats for Valuations

4

Getting the Output

5

Summary

SPNLP: From Syntax to Model Checking Lascarides & Klein Outline Review Computational Framework Alternative Input Formats for Valuations Getting the Output Summary

Logical Syntax and Semantics

A logical language based on:

1 function-argument structures: (M N) 2 lambda abstraction: λx.(α x) 3 beta-reduction: (λx.(M x) N) ≡ (M N) 4 Boolean combinations: (φ ∧ ψ), . . . 5 Quantified formulas: ∀x.φ, ∃x.φ

Models for the language:

1 M = D, V 2 variable assignment g : Var → D 3 recursive definition of [

[α] ]M,g for expressions α.

4 M, g |

= φ iff [ [φ] ]M,g′ = 1.

SPNLP: From Syntax to Model Checking Lascarides & Klein Outline Review Computational Framework Alternative Input Formats for Valuations Getting the Output Summary

Logical Syntax and Semantics

A logical language based on:

1 function-argument structures: (M N) 2 lambda abstraction: λx.(α x) 3 beta-reduction: (λx.(M x) N) ≡ (M N) 4 Boolean combinations: (φ ∧ ψ), . . . 5 Quantified formulas: ∀x.φ, ∃x.φ

Models for the language:

1 M = D, V 2 variable assignment g : Var → D 3 recursive definition of [

[α] ]M,g for expressions α.

4 M, g |

= φ iff [ [φ] ]M,g′ = 1.

SPNLP: From Syntax to Model Checking Lascarides & Klein Outline Review Computational Framework Alternative Input Formats for Valuations Getting the Output Summary

Logical Syntax and Semantics

A logical language based on:

1 function-argument structures: (M N) 2 lambda abstraction: λx.(α x) 3 beta-reduction: (λx.(M x) N) ≡ (M N) 4 Boolean combinations: (φ ∧ ψ), . . . 5 Quantified formulas: ∀x.φ, ∃x.φ

Models for the language:

1 M = D, V 2 variable assignment g : Var → D 3 recursive definition of [

[α] ]M,g for expressions α.

4 M, g |

= φ iff [ [φ] ]M,g′ = 1.

SPNLP: From Syntax to Model Checking Lascarides & Klein Outline Review Computational Framework Alternative Input Formats for Valuations Getting the Output Summary

Logical Syntax and Semantics

A logical language based on:

1 function-argument structures: (M N) 2 lambda abstraction: λx.(α x) 3 beta-reduction: (λx.(M x) N) ≡ (M N) 4 Boolean combinations: (φ ∧ ψ), . . . 5 Quantified formulas: ∀x.φ, ∃x.φ

Models for the language:

1 M = D, V 2 variable assignment g : Var → D 3 recursive definition of [

[α] ]M,g for expressions α.

4 M, g |

= φ iff [ [φ] ]M,g′ = 1.

SPNLP: From Syntax to Model Checking Lascarides & Klein Outline Review Computational Framework Alternative Input Formats for Valuations Getting the Output Summary

Logical Syntax and Semantics

A logical language based on:

1 function-argument structures: (M N) 2 lambda abstraction: λx.(α x) 3 beta-reduction: (λx.(M x) N) ≡ (M N) 4 Boolean combinations: (φ ∧ ψ), . . . 5 Quantified formulas: ∀x.φ, ∃x.φ

Models for the language:

1 M = D, V 2 variable assignment g : Var → D 3 recursive definition of [

[α] ]M,g for expressions α.

4 M, g |

= φ iff [ [φ] ]M,g′ = 1.

SPNLP: From Syntax to Model Checking Lascarides & Klein Outline Review Computational Framework Alternative Input Formats for Valuations Getting the Output Summary

Logical Syntax and Semantics

A logical language based on:

1 function-argument structures: (M N) 2 lambda abstraction: λx.(α x) 3 beta-reduction: (λx.(M x) N) ≡ (M N) 4 Boolean combinations: (φ ∧ ψ), . . . 5 Quantified formulas: ∀x.φ, ∃x.φ

Models for the language:

1 M = D, V 2 variable assignment g : Var → D 3 recursive definition of [

[α] ]M,g for expressions α.

4 M, g |

= φ iff [ [φ] ]M,g′ = 1.

SPNLP: From Syntax to Model Checking Lascarides & Klein Outline Review Computational Framework Alternative Input Formats for Valuations Getting the Output Summary

Logical Syntax and Semantics

A logical language based on:

1 function-argument structures: (M N) 2 lambda abstraction: λx.(α x) 3 beta-reduction: (λx.(M x) N) ≡ (M N) 4 Boolean combinations: (φ ∧ ψ), . . . 5 Quantified formulas: ∀x.φ, ∃x.φ

Models for the language:

1 M = D, V 2 variable assignment g : Var → D 3 recursive definition of [

[α] ]M,g for expressions α.

4 M, g |

= φ iff [ [φ] ]M,g′ = 1.

SPNLP: From Syntax to Model Checking Lascarides & Klein Outline Review Computational Framework Alternative Input Formats for Valuations Getting the Output Summary

Logical Syntax and Semantics

A logical language based on:

1 function-argument structures: (M N) 2 lambda abstraction: λx.(α x) 3 beta-reduction: (λx.(M x) N) ≡ (M N) 4 Boolean combinations: (φ ∧ ψ), . . . 5 Quantified formulas: ∀x.φ, ∃x.φ

Models for the language:

1 M = D, V 2 variable assignment g : Var → D 3 recursive definition of [

[α] ]M,g for expressions α.

4 M, g |

= φ iff [ [φ] ]M,g′ = 1.

SPNLP: From Syntax to Model Checking Lascarides & Klein Outline Review Computational Framework Alternative Input Formats for Valuations Getting the Output Summary

Logical Syntax and Semantics

A logical language based on:

1 function-argument structures: (M N) 2 lambda abstraction: λx.(α x) 3 beta-reduction: (λx.(M x) N) ≡ (M N) 4 Boolean combinations: (φ ∧ ψ), . . . 5 Quantified formulas: ∀x.φ, ∃x.φ

Models for the language:

1 M = D, V 2 variable assignment g : Var → D 3 recursive definition of [

[α] ]M,g for expressions α.

4 M, g |

= φ iff [ [φ] ]M,g′ = 1.

SPNLP: From Syntax to Model Checking Lascarides & Klein Outline Review Computational Framework Alternative Input Formats for Valuations Getting the Output Summary

Logical Syntax and Semantics

A logical language based on:

1 function-argument structures: (M N) 2 lambda abstraction: λx.(α x) 3 beta-reduction: (λx.(M x) N) ≡ (M N) 4 Boolean combinations: (φ ∧ ψ), . . . 5 Quantified formulas: ∀x.φ, ∃x.φ

Models for the language:

1 M = D, V 2 variable assignment g : Var → D 3 recursive definition of [

[α] ]M,g for expressions α.

4 M, g |

= φ iff [ [φ] ]M,g′ = 1.

SPNLP: From Syntax to Model Checking Lascarides & Klein Outline Review Computational Framework Alternative Input Formats for Valuations Getting the Output Summary

Logical Syntax and Semantics

A logical language based on:

1 function-argument structures: (M N) 2 lambda abstraction: λx.(α x) 3 beta-reduction: (λx.(M x) N) ≡ (M N) 4 Boolean combinations: (φ ∧ ψ), . . . 5 Quantified formulas: ∀x.φ, ∃x.φ

Models for the language:

1 M = D, V 2 variable assignment g : Var → D 3 recursive definition of [

[α] ]M,g for expressions α.

4 M, g |

= φ iff [ [φ] ]M,g′ = 1.

SPNLP: From Syntax to Model Checking Lascarides & Klein Outline Review Computational Framework Alternative Input Formats for Valuations Getting the Output Summary

Compositional Semantics

Compositionality The meaning of a complex expression is a function of the meaning of its parts. How do we know what the parts are? Feature-based context-free grammar formalism. Every category has a sem feature whose value is the semantics of expressions of that category:

lexical categories: fully-instantiated LF. phrasal categories: build an LF by function application

• ver the LFs of the daughters.

Example PS Rule

❙❬s❡♠ ❂ ❁❛♣♣✭❄s✉❜❥✱❄✈♣✮❃❪ ✲❃ ◆P❬s❡♠❂❄s✉❜❥❪ ❱P❬s❡♠❂❄✈♣❪

SPNLP: From Syntax to Model Checking Lascarides & Klein Outline Review Computational Framework Alternative Input Formats for Valuations Getting the Output Summary

Compositional Semantics

Compositionality The meaning of a complex expression is a function of the meaning of its parts. How do we know what the parts are? Feature-based context-free grammar formalism. Every category has a sem feature whose value is the semantics of expressions of that category:

lexical categories: fully-instantiated LF. phrasal categories: build an LF by function application

• ver the LFs of the daughters.

Example PS Rule

❙❬s❡♠ ❂ ❁❛♣♣✭❄s✉❜❥✱❄✈♣✮❃❪ ✲❃ ◆P❬s❡♠❂❄s✉❜❥❪ ❱P❬s❡♠❂❄✈♣❪

SPNLP: From Syntax to Model Checking Lascarides & Klein Outline Review Computational Framework Alternative Input Formats for Valuations Getting the Output Summary

Compositional Semantics

Compositionality The meaning of a complex expression is a function of the meaning of its parts. How do we know what the parts are? Feature-based context-free grammar formalism. Every category has a sem feature whose value is the semantics of expressions of that category:

lexical categories: fully-instantiated LF. phrasal categories: build an LF by function application

• ver the LFs of the daughters.

Example PS Rule

❙❬s❡♠ ❂ ❁❛♣♣✭❄s✉❜❥✱❄✈♣✮❃❪ ✲❃ ◆P❬s❡♠❂❄s✉❜❥❪ ❱P❬s❡♠❂❄✈♣❪

SPNLP: From Syntax to Model Checking Lascarides & Klein Outline Review Computational Framework Alternative Input Formats for Valuations Getting the Output Summary

Compositional Semantics

Compositionality The meaning of a complex expression is a function of the meaning of its parts. How do we know what the parts are? Feature-based context-free grammar formalism. Every category has a sem feature whose value is the semantics of expressions of that category:

lexical categories: fully-instantiated LF. phrasal categories: build an LF by function application

• ver the LFs of the daughters.

Example PS Rule

❙❬s❡♠ ❂ ❁❛♣♣✭❄s✉❜❥✱❄✈♣✮❃❪ ✲❃ ◆P❬s❡♠❂❄s✉❜❥❪ ❱P❬s❡♠❂❄✈♣❪

SPNLP: From Syntax to Model Checking Lascarides & Klein Outline Review Computational Framework Alternative Input Formats for Valuations Getting the Output Summary

Compositional Semantics

Compositionality The meaning of a complex expression is a function of the meaning of its parts. How do we know what the parts are? Feature-based context-free grammar formalism. Every category has a sem feature whose value is the semantics of expressions of that category:

lexical categories: fully-instantiated LF. phrasal categories: build an LF by function application

• ver the LFs of the daughters.

Example PS Rule

❙❬s❡♠ ❂ ❁❛♣♣✭❄s✉❜❥✱❄✈♣✮❃❪ ✲❃ ◆P❬s❡♠❂❄s✉❜❥❪ ❱P❬s❡♠❂❄✈♣❪

SPNLP: From Syntax to Model Checking Lascarides & Klein Outline Review Computational Framework Alternative Input Formats for Valuations Getting the Output Summary

Compositional Semantics

Compositionality The meaning of a complex expression is a function of the meaning of its parts. How do we know what the parts are? Feature-based context-free grammar formalism. Every category has a sem feature whose value is the semantics of expressions of that category:

lexical categories: fully-instantiated LF. phrasal categories: build an LF by function application

• ver the LFs of the daughters.

Example PS Rule

❙❬s❡♠ ❂ ❁❛♣♣✭❄s✉❜❥✱❄✈♣✮❃❪ ✲❃ ◆P❬s❡♠❂❄s✉❜❥❪ ❱P❬s❡♠❂❄✈♣❪

SPNLP: From Syntax to Model Checking Lascarides & Klein Outline Review Computational Framework Alternative Input Formats for Valuations Getting the Output Summary

Computational Recap

Logical expressions are parsed into subclasses of ❊①♣r❡ss✐♦♥ by ♥❧t❦✳s❡♠✳❧♦❣✐❝. Expressions can be evaluated in a model by ♥❧t❦✳s❡♠✳❡✈❛❧✉❛t❡. English sentences can be parsed into LFs by ♥❧t❦✳♣❛rs❡✳❢❡❛t✉r❡❝❤❛rt (via the ♥❧t❦✳♣❛rs❡✳❧♦❛❞❴❡❛r❧❡②✭✮ function.) Sample Interpretation A dog barks − → ∃x.((dog x) ∧ (bark x)) − → [ [∃x.((dog x) ∧ (bark x)] ]M,g = 1iff . . .

SPNLP: From Syntax to Model Checking Lascarides & Klein Outline Review Computational Framework Alternative Input Formats for Valuations Getting the Output Summary

Computational Recap

Logical expressions are parsed into subclasses of ❊①♣r❡ss✐♦♥ by ♥❧t❦✳s❡♠✳❧♦❣✐❝. Expressions can be evaluated in a model by ♥❧t❦✳s❡♠✳❡✈❛❧✉❛t❡. English sentences can be parsed into LFs by ♥❧t❦✳♣❛rs❡✳❢❡❛t✉r❡❝❤❛rt (via the ♥❧t❦✳♣❛rs❡✳❧♦❛❞❴❡❛r❧❡②✭✮ function.) Sample Interpretation A dog barks − → ∃x.((dog x) ∧ (bark x)) − → [ [∃x.((dog x) ∧ (bark x)] ]M,g = 1iff . . .

SPNLP: From Syntax to Model Checking Lascarides & Klein Outline Review Computational Framework Alternative Input Formats for Valuations Getting the Output Summary

Computational Recap

Logical expressions are parsed into subclasses of ❊①♣r❡ss✐♦♥ by ♥❧t❦✳s❡♠✳❧♦❣✐❝. Expressions can be evaluated in a model by ♥❧t❦✳s❡♠✳❡✈❛❧✉❛t❡. English sentences can be parsed into LFs by ♥❧t❦✳♣❛rs❡✳❢❡❛t✉r❡❝❤❛rt (via the ♥❧t❦✳♣❛rs❡✳❧♦❛❞❴❡❛r❧❡②✭✮ function.) Sample Interpretation A dog barks − → ∃x.((dog x) ∧ (bark x)) − → [ [∃x.((dog x) ∧ (bark x)] ]M,g = 1iff . . .

SPNLP: From Syntax to Model Checking Lascarides & Klein Outline Review Computational Framework Alternative Input Formats for Valuations Getting the Output Summary

Computational Recap

Logical expressions are parsed into subclasses of ❊①♣r❡ss✐♦♥ by ♥❧t❦✳s❡♠✳❧♦❣✐❝. Expressions can be evaluated in a model by ♥❧t❦✳s❡♠✳❡✈❛❧✉❛t❡. English sentences can be parsed into LFs by ♥❧t❦✳♣❛rs❡✳❢❡❛t✉r❡❝❤❛rt (via the ♥❧t❦✳♣❛rs❡✳❧♦❛❞❴❡❛r❧❡②✭✮ function.) Sample Interpretation A dog barks − → ∃x.((dog x) ∧ (bark x)) − → [ [∃x.((dog x) ∧ (bark x)] ]M,g = 1iff . . .

SPNLP: From Syntax to Model Checking Lascarides & Klein Outline Review Computational Framework Alternative Input Formats for Valuations Getting the Output Summary

Parsing

✐♠♣♦rt ♥❧t❦ t♦❦❡♥s ❂ ✬❛ ❞♦❣ ❜❛r❦s✬✳s♣❧✐t✭✮ ❢r♦♠ ♥❧t❦✳♣❛rs❡ ✐♠♣♦rt ❧♦❛❞❴❡❛r❧❡② ❝♣ ❂ ❧♦❛❞❴❡❛r❧❡②✭✬❣r❛♠♠❛rs✴s❡♠✶✳❢❝❢❣✬✱ tr❛❝❡❂✵✮ tr❡❡s ❂ ❝♣✳♥❜❡st❴♣❛rs❡✭t♦❦❡♥s✮ ❢♦r t ✐♥ tr❡❡s✿ ♣r✐♥t t

SPNLP: From Syntax to Model Checking Lascarides & Klein Outline Review Computational Framework Alternative Input Formats for Valuations Getting the Output Summary

Parsing Output

Parse for A dog barks ✭❙❬s❡♠❂❁s♦♠❡ ①✳✭❛♥❞ ✭❞♦❣ ①✮ ✭❜❛r❦ ①✮✮❃❪ ✭◆P❬s❡♠❂❁❭P✳s♦♠❡ ①✳✭❛♥❞ ✭❞♦❣ ①✮ ✭P ①✮✮❃❪ ✭❉❡t❬s❡♠❂❁❭◗ P✳s♦♠❡ ①✳✭❛♥❞ ✭◗ ①✮ ✭P ①✮✮❃❪ ❛✮ ✭◆❬s❡♠❂❁❞♦❣❃❪ ❞♦❣✮✮ ✭❱P❬s❡♠❂❁❭①✳✭❜❛r❦ ①✮❃❪ ✭■❱❬s❡♠❂❁❭①✳✭❜❛r❦ ①✮❃❪ ❜❛r❦s✮✮✮

SPNLP: From Syntax to Model Checking Lascarides & Klein Outline Review Computational Framework Alternative Input Formats for Valuations Getting the Output Summary

Declaring a Model

Model for A dog barks ❢r♦♠ ♥❧t❦✳s❡♠ ✐♠♣♦rt ✯ ✈❛❧ ❂ ❱❛❧✉❛t✐♦♥✭④ ✬❢✐❞♦✬✿ ✬❢✬✱ ✬❞♦❣✬✿ ④✬❢✬✿ ❚r✉❡✱ ✬❞✬✿ ❚r✉❡⑥✱ ✬❜❛r❦✬✿ ④✬❞✬✿ ❚r✉❡⑥✱ ⑥✮ ❞♦♠ ❂ ✈❛❧✳❞♦♠❛✐♥ ♠ ❂ ▼♦❞❡❧✭❞♦♠✱ ✈❛❧✮ ❣ ❂ ❆ss✐❣♥♠❡♥t✭❞♦♠✮

SPNLP: From Syntax to Model Checking Lascarides & Klein Outline Review Computational Framework Alternative Input Formats for Valuations Getting the Output Summary

Model Checking

Truth in model ♠ ❃❃❃ ♣r✐♥t ♠ ❉♦♠❛✐♥ ❂ s❡t✭❬✬❞✬✱ ✬❢✬❪✮✱ ❱❛❧✉❛t✐♦♥ ❂ ④✬❜❛r❦✬✿ ④✬❞✬✿ ❚r✉❡⑥✱ ✬❞♦❣✬✿ ④✬❞✬✿ ❚r✉❡✱ ✬❢✬✿ ❚r✉❡⑥✱ ✬❢✐❞♦✬✿ ✬❢✬⑥ ❃❃❃ ❣ ④⑥ ❃❃❃ ♠✳❡✈❛❧✉❛t❡✭✬s♦♠❡ ①✳ ✭✭❞♦❣ ①✮ ❛♥❞ ✭❜❛r❦ ①✮✮✬✱ ❣✮ ❚r✉❡

SPNLP: From Syntax to Model Checking Lascarides & Klein Outline Review Computational Framework Alternative Input Formats for Valuations Getting the Output Summary

Tracing

Truth in model ♠

❃❃❃ ♠✳❡✈❛❧✉❛t❡✭✬s♦♠❡ ①✳✭✭❞♦❣ ①✮ ❛♥❞ ✭❜❛r❦ ①✮✮✬✱❣✱tr❛❝❡❂✶✮ ❖♣❡♥ ❢♦r♠✉❧❛ ✐s ✬✭❛♥❞ ✭❞♦❣ ①✮ ✭❜❛r❦ ①✮✮✬ ✇✐t❤ ❛ss✐❣♥♠❡♥t ❣ ✭tr②✐♥❣ ❛ss✐❣♥♠❡♥t ❣❬❞✴①❪✮ ✈❛❧✉❡ ♦❢ ✬✭❛♥❞ ✭❞♦❣ ①✮ ✭❜❛r❦ ①✮✮✬ ✉♥❞❡r ❣❬❞✴①❪ ✐s ❚r✉❡ ✭tr②✐♥❣ ❛ss✐❣♥♠❡♥t ❣❬❢✴①❪✮ ✈❛❧✉❡ ♦❢ ✬✭❛♥❞ ✭❞♦❣ ①✮ ✭❜❛r❦ ①✮✮✬ ✉♥❞❡r ❣❬❢✴①❪ ✐s ❋❛❧s❡ ✬✭❛♥❞ ✭❞♦❣ ①✮ ✭❜❛r❦ ①✮✮✬ ❡✈❛❧✉❛t❡s t♦ ❚r✉❡ ✉♥❞❡r ▼✱ ❣ ✬s♦♠❡ ①✳ ✭✭❞♦❣ ①✮ ❛♥❞ ✭❜❛r❦ ①✮✮✬ ❡✈❛❧✉❛t❡s t♦ ❚r✉❡ ✉♥❞❡r ▼✱ ❣

SPNLP: From Syntax to Model Checking Lascarides & Klein Outline Review Computational Framework Alternative Input Formats for Valuations Getting the Output Summary

Inputting Valuations: Vanilla Method

❢r♦♠ ♥❧t❦✳s❡♠ ✐♠♣♦rt ✯ ✈❛❧ ❂ ❱❛❧✉❛t✐♦♥✭④ ✬❢✐❞♦✬✿ ✬❢✬✱ ✬❦✐♠✬✿ ✬❦✬ ✬❝❤❛s❡✬✿ ④✬❢✬✿ ④✬❦✬✿ ❚r✉❡⑥✱ ✬❦✬✿ ④✬❢✬✿ ❚r✉❡⑥⑥ ⑥✮ ❞♦♠ ❂ ✈❛❧✳❞♦♠❛✐♥ ♠ ❂ ▼♦❞❡❧✭❞♦♠✱ ✈❛❧✮ ❣ ❂ ❆ss✐❣♥♠❡♥t✭❞♦♠✮

SPNLP: From Syntax to Model Checking Lascarides & Klein Outline Review Computational Framework Alternative Input Formats for Valuations Getting the Output Summary

Inputting Valuations: Read in tuples

❢r♦♠ ♥❧t❦✳s❡♠ ✐♠♣♦rt ✯ ✈❛❧ ❂ ❱❛❧✉❛t✐♦♥✭✮ ✈ ❂ ❬✭✬❢✐❞♦✬✱ ✬❢✬✮✱ ✭✬❦✐♠✬✱ ✬❦✬✮✱ ✭✬❝❤❛s❡✬✱ s❡t✭❬✭✬❢✬✱ ✬❦✬✮✱ ✭✬❦✬✱ ✬❢✬✮❪✮✮ ❪ ✈❛❧✳r❡❛❞✭✈✮ ❞♦♠ ❂ ✈❛❧✳❞♦♠❛✐♥ ♠ ❂ ▼♦❞❡❧✭❞♦♠✱ ✈❛❧✮ ❣ ❂ ❆ss✐❣♥♠❡♥t✭❞♦♠✮

SPNLP: From Syntax to Model Checking Lascarides & Klein Outline Review Computational Framework Alternative Input Formats for Valuations Getting the Output Summary

Inputting Valuations: Read from string (or file)

❢r♦♠ ♥❧t❦✳s❡♠ ✐♠♣♦rt ✯ ✈ ❂ ✧✧✧ ❢✐❞♦ ❂❃ ❢ ❦✐♠ ❂❃ ❦ ❝❤❛s❡ ❂❃ ④✭❢✱ ❦✮✱ ✭❦✱ ❢✮⑥ ✧✧✧ ✈❛❧ ❂ ♣❛rs❡❴✈❛❧✉❛t✐♦♥✭✈✮ ❞♦♠ ❂ ✈❛❧✳❞♦♠❛✐♥ ♠ ❂ ▼♦❞❡❧✭❞♦♠✱ ✈❛❧✮ ❣ ❂ ❆ss✐❣♥♠❡♥t✭❞♦♠✮

SPNLP: From Syntax to Model Checking Lascarides & Klein Outline Review Computational Framework Alternative Input Formats for Valuations Getting the Output Summary

Examining Valuations

Outputting tuples ❃❃❃ ✈❛❧ ④✬❢✬✿ ✬❢✬✱ ✬❦✐♠✬✿ ✬❦✬✱ ✬❝❤❛s❡✬✿ ④✬❦✬✿ ④✬❢✬✿ ❚r✉❡⑥✱ ✬❢✬✿ ④✬❦✬✿ ❚r✉❡⑥⑥⑥ ❃❃❃ r❡❧❛t✐♦♥ ❂ ✈❛❧❬✬❝❤❛s❡✬❪ ❃❃❃ r❡❧❛t✐♦♥ ④✬❦✬✿ ④✬❢✬✿ ❚r✉❡⑥✱ ✬❢✬✿ ④✬❦✬✿ ❚r✉❡⑥⑥ ❃❃❃ r❡❧❛t✐♦♥✳t✉♣❧❡s✭✮ s❡t✭❬✭✬❦✬✱ ✬❢✬✮✱ ✭✬❢✬✱ ✬❦✬✮❪✮ ❃❃❃ ✈❛❧❬✬r✉♥✬❪ ❚r❛❝❡❜❛❝❦ ✭♠♦st r❡❝❡♥t ❝❛❧❧ ❧❛st✮✿ ✳✳✳ ♥❧t❦✳s❡♠✳❡✈❛❧✉❛t❡✳❯♥❞❡❢✐♥❡❞✿ ❯♥❦♥♦✇♥ ❡①♣r❡ss✐♦♥✿ ✬r✉♥✬ ❃❃❃ ♠✳❡✈❛❧✉❛t❡✭✬❭❭①✳ ✭❝❤❛s❡ ① ❦✐♠✮✬✱ ❣✮ ④✬❢✬✿ ❚r✉❡⑥ ❃❃❃ ♠✳❡✈❛❧✉❛t❡✭✬❭❭①✳ s♦♠❡ ②✳ ✭❝❤❛s❡ ① ②✮✬✱ ❣✮✳t✉♣❧❡s✭✮ s❡t✭❬✬❦✬✱ ✬❢✬❪✮

SPNLP: From Syntax to Model Checking Lascarides & Klein Outline Review Computational Framework Alternative Input Formats for Valuations Getting the Output Summary

Mapping from Syntax to Semantics, 1

Parse sentence & load valuation

❢r♦♠ ♥❧t❦✳♣❛rs❡ ✐♠♣♦rt ❋❡❛t✉r❡❊❛r❧❡②❈❤❛rtP❛rs❡r ✐♠♣♦rt ♥❧t❦✳❞❛t❛ ❣r❛♠♠❛r ❂ ♥❧t❦✳❞❛t❛✳❧♦❛❞✭✬❣r❛♠♠❛rs✴s❡♠✷✳❢❝❢❣✬✮ ✈❛❧ ❂ ♥❧t❦✳❞❛t❛✳❧♦❛❞✭✬❣r❛♠♠❛rs✴✈❛❧✉❛t✐♦♥✶✳✈❛❧✬✮ ❞♦♠ ❂ ✈❛❧✳❞♦♠❛✐♥ ♠ ❂ ▼♦❞❡❧✭❞♦♠✱ ✈❛❧✮ ❣ ❂ ❆ss✐❣♥♠❡♥t✭❞♦♠✮ s❡♥t ❂ ✬s♦♠❡ ❣✐r❧ ❝❤❛s❡s ❛ ❞♦❣✬ r❡s✉❧t ❂ ♥❧t❦✳s❡♠✳t❡①t❴❡✈❛❧✉❛t❡✭❬s❡♥t❪✱ ❣r❛♠♠❛r✱ ♠✱ ❣✮ ❢♦r ✭s②♥tr❡❡✱ s❡♠r❡♣✱ ✈❛❧✉❡✮ ✐♥ r❡s✉❧t❬s❡♥t❪✿ ♣r✐♥t ✧✬✪s✬ ✐s ✪s ✐♥ ▼♦❞❡❧ ♠❭♥✧ ✪ ✭s❡♠r❡♣✳✐♥❢✐①✐❢②✭✮✱ ✈❛❧✉❡✮

SPNLP: From Syntax to Model Checking Lascarides & Klein Outline Review Computational Framework Alternative Input Formats for Valuations Getting the Output Summary

Mapping from Syntax to Semantics, 2

Result ✬s♦♠❡ ①✳✭✭❣✐r❧ ①✮ ❛♥❞ s♦♠❡ ③✺✺✾✳✭✭❞♦❣ ③✺✺✾✮ ❛♥❞ ✭❝❤❛s❡ ③✺✺✾ ①✮✮✮✬ ✐s ❚r✉❡ ✐♥ ▼♦❞❡❧ ♠

SPNLP: From Syntax to Model Checking Lascarides & Klein Outline Review Computational Framework Alternative Input Formats for Valuations Getting the Output Summary

Summary

The NLTK implementation yields an end-to-end mapping:

Compute all parses of a sentence S relative to a feature-based CFG; provide a logical form for each constituent of S; parse the logical form LF for each reading of S; build a representation of a first order model M; recursively evaluate LF in M. If LF contains free variables, then value also depends

• n g.

Major shortcoming so far: no treatment of semantic ambiguity, e.g., quantifier scope ambiguity. Two approaches in ♥❧t❦✳❝♦♥tr✐❜: ❤♦❧❡✳♣② and ❣❧✉❡s❡♠❛♥t✐❝s package.

SPNLP: From Syntax to Model Checking Lascarides & Klein Outline Review Computational Framework Alternative Input Formats for Valuations Getting the Output Summary

Summary

The NLTK implementation yields an end-to-end mapping:

Compute all parses of a sentence S relative to a feature-based CFG; provide a logical form for each constituent of S; parse the logical form LF for each reading of S; build a representation of a first order model M; recursively evaluate LF in M. If LF contains free variables, then value also depends

• n g.

Major shortcoming so far: no treatment of semantic ambiguity, e.g., quantifier scope ambiguity. Two approaches in ♥❧t❦✳❝♦♥tr✐❜: ❤♦❧❡✳♣② and ❣❧✉❡s❡♠❛♥t✐❝s package.

SPNLP: From Syntax to Model Checking Lascarides & Klein Outline Review Computational Framework Alternative Input Formats for Valuations Getting the Output Summary

Summary

The NLTK implementation yields an end-to-end mapping:

Compute all parses of a sentence S relative to a feature-based CFG; provide a logical form for each constituent of S; parse the logical form LF for each reading of S; build a representation of a first order model M; recursively evaluate LF in M. If LF contains free variables, then value also depends

• n g.

Major shortcoming so far: no treatment of semantic ambiguity, e.g., quantifier scope ambiguity. Two approaches in ♥❧t❦✳❝♦♥tr✐❜: ❤♦❧❡✳♣② and ❣❧✉❡s❡♠❛♥t✐❝s package.

SPNLP: From Syntax to Model Checking Lascarides & Klein Outline Review Computational Framework Alternative Input Formats for Valuations Getting the Output Summary

Summary

The NLTK implementation yields an end-to-end mapping:

Compute all parses of a sentence S relative to a feature-based CFG; provide a logical form for each constituent of S; parse the logical form LF for each reading of S; build a representation of a first order model M; recursively evaluate LF in M. If LF contains free variables, then value also depends

• n g.

Major shortcoming so far: no treatment of semantic ambiguity, e.g., quantifier scope ambiguity. Two approaches in ♥❧t❦✳❝♦♥tr✐❜: ❤♦❧❡✳♣② and ❣❧✉❡s❡♠❛♥t✐❝s package.

SPNLP: From Syntax to Model Checking Lascarides & Klein Outline Review Computational Framework Alternative Input Formats for Valuations Getting the Output Summary

Summary

The NLTK implementation yields an end-to-end mapping:

Compute all parses of a sentence S relative to a feature-based CFG; provide a logical form for each constituent of S; parse the logical form LF for each reading of S; build a representation of a first order model M; recursively evaluate LF in M. If LF contains free variables, then value also depends

• n g.

Major shortcoming so far: no treatment of semantic ambiguity, e.g., quantifier scope ambiguity. Two approaches in ♥❧t❦✳❝♦♥tr✐❜: ❤♦❧❡✳♣② and ❣❧✉❡s❡♠❛♥t✐❝s package.

SPNLP: From Syntax to Model Checking Lascarides & Klein Outline Review Computational Framework Alternative Input Formats for Valuations Getting the Output Summary

Summary

The NLTK implementation yields an end-to-end mapping:

Compute all parses of a sentence S relative to a feature-based CFG; provide a logical form for each constituent of S; parse the logical form LF for each reading of S; build a representation of a first order model M; recursively evaluate LF in M. If LF contains free variables, then value also depends

• n g.

Major shortcoming so far: no treatment of semantic ambiguity, e.g., quantifier scope ambiguity. Two approaches in ♥❧t❦✳❝♦♥tr✐❜: ❤♦❧❡✳♣② and ❣❧✉❡s❡♠❛♥t✐❝s package.

SPNLP: From Syntax to Model Checking Lascarides & Klein Outline Review Computational Framework Alternative Input Formats for Valuations Getting the Output Summary

Summary

The NLTK implementation yields an end-to-end mapping:

Compute all parses of a sentence S relative to a feature-based CFG; provide a logical form for each constituent of S; parse the logical form LF for each reading of S; build a representation of a first order model M; recursively evaluate LF in M. If LF contains free variables, then value also depends

• n g.

Major shortcoming so far: no treatment of semantic ambiguity, e.g., quantifier scope ambiguity. Two approaches in ♥❧t❦✳❝♦♥tr✐❜: ❤♦❧❡✳♣② and ❣❧✉❡s❡♠❛♥t✐❝s package.

SPNLP: From Syntax to Model Checking Lascarides & Klein Outline Review Computational Framework Alternative Input Formats for Valuations Getting the Output Summary

Summary

The NLTK implementation yields an end-to-end mapping:

Compute all parses of a sentence S relative to a feature-based CFG; provide a logical form for each constituent of S; parse the logical form LF for each reading of S; build a representation of a first order model M; recursively evaluate LF in M. If LF contains free variables, then value also depends

• n g.

Major shortcoming so far: no treatment of semantic ambiguity, e.g., quantifier scope ambiguity. Two approaches in ♥❧t❦✳❝♦♥tr✐❜: ❤♦❧❡✳♣② and ❣❧✉❡s❡♠❛♥t✐❝s package.

SPNLP: From Syntax to Model Checking Lascarides & Klein Outline Review Computational Framework Alternative Input Formats for Valuations Getting the Output Summary

Summary

The NLTK implementation yields an end-to-end mapping:

Compute all parses of a sentence S relative to a feature-based CFG; provide a logical form for each constituent of S; parse the logical form LF for each reading of S; build a representation of a first order model M; recursively evaluate LF in M. If LF contains free variables, then value also depends

• n g.

Major shortcoming so far: no treatment of semantic ambiguity, e.g., quantifier scope ambiguity. Two approaches in ♥❧t❦✳❝♦♥tr✐❜: ❤♦❧❡✳♣② and ❣❧✉❡s❡♠❛♥t✐❝s package.