First Order Predicate Logic to English Translation

Overview

Natural Language Generation First Order Predicate Logic to English Translation

Natural Language Generation

Content Determination Document Structuring Sentence Aggregation Referring Expression Generation

Content Determination

The process of deciding what to say Different communicative goals may require different

information to be expressed Content required may depend on characteristics of

the reader Constraints upon the output Questions of what information should be included are

application dependent

Examples

How Good are we?

Mobile is still working

STOP Don’t Let them Go http://www.youtube.com/watch?v=nfng7QHIU0Y

Document Structuring

Problem of imposing ordering and structure over the information

A text is not just a random collection of sentences Texts have an underlying structure in which the parts

are related together Readers have an expectation of the structure of text Two related issues:

– conceptual grouping– rhetorical relationships

Examples

I am dead

Burn the CD

Ok, Lets see

First Order Predicate Logic to English Translation System Description Outline of Method Universal Quantifiers Existential Quantifiers Example Translation of Single Quantifiers Translation of Single Quantifiers using IMPLY Translation of Double Quantifiers Translation of Double Quantifiers using IMPLY CatchAll Function

Universal Quantifiers

For every person x, All persons Everyone For every person x, if Every person Every person who

Existential Quantifiers

There exists a person x such that There exists a person who Someone There exists a person x such that if There exists a person who Some

Example

\A x [J(x) V K(x)] J(x) = x studies hard K(x) = x loves sports

Translation of Single Quantifiers

J(x) = x studies hard K(x) = x loves sports \A x [J(x) V K(x)]

– For every person x, x studies hard or loves sports– All persons study hard or love sports– Everyone studies hard or loves sports

Translation of Single Quantifiers

J(x) = x studies hard K(x) = x loves sports \E x [J(x) ^ K(x)]

– There exists a person x such that x studies hard and loves sports

– There exists a person who studies hard and love sports

– Someone studies hard and loves sports

Translation of Single Quantifiers

J(x) = x studies hard K(x) = x loves sports \E x [J(x) V ~K(x)]

– There exists a person x such that x studies hard or does not love sports

– There exists a person who studies hard or does not love sports

– Someone studies hard or does not love sports

Translation of Single Quantifiers using IMPLY J(x) = x studies hard K(x) = x loves sports \A x [J(x) -> K(x)]

– For every person x, if x studies hard, x loves sports

– Every person loves sports if he/she studies hard

Translation of Single Quantifiers using IMPLY J(x) = x studies hard K(x) = x loves sports \E x [J(x) -> K(x)]

– There exists a person x such that if x studies hard, x loves sports

– There exists a person who loves sports if he/she studies hard

Translation of Single Quantifiers using IMPLY J(x) = x studies hard K(x) = x loves sports \E x [J(x) -> ~K(x)]

– There exists a person x such that if x studies hard, x does not love sports

– There exists a person who does not love sports if he/she studies hard

Translation of Double Quantifiers

P(x,y) = x runs faster than y Q(x,y) = x is older than y \A x [P(x,y) V Q(x,y)]

– For every person x the following holds: x runs faster than y or x is older than y

Translation of Double Quantifiers

P(x,y) = x runs faster than y Q(x,y) = x is older than y \E x [P(x,y) ^ Q(x,y)]

– There exist a person x which satisfies the following: x runs faster than y and x is older than y

Translation of Double Quantifiers

P(x,y) = x runs faster than y Q(x,y) = x is older than y \E x [P(x,y) V ~Q(x,y)]

– There exist a person x which satisfies the following: x run faster than y or x is not older than y

Translation of Double Quantifiers using IMPLY R(x,y) = x swims faster than y J(y) = y studies hard K(x) = x loves sports \A x \E y [[K(x) ^ J(y)] -> R(x,y)]

– For every person x and for some person y the following holds: If x loves sports and y studies hard then x swims faster than y

Translation of Double Quantifiers using IMPLY R(x,y) = x swims faster than y L(x) = x is a student \E x \A y [R(x,y) -> L(x)]

– There exist a person x for every person y which satisfies the following: If x swims faster than y then x is a student

Translation of Double Quantifiers using IMPLY S(x,y) = x is taller than y \E y \E x ~S(y,x)

– There exist a person y which satisfies the following: some person y is not taller than x

Implication

P(x,y) = x runs faster than y S(x,y) = x is taller than y \A x [P(x,y) -> S(x,y)]

– For every person x the following holds: x runs faster than y implies x is taller than y

Implication

P(x,y) = x runs faster than y Q(x,y) = x is older than y T(x,y) = x talks louder than y \E x [P(x,y) ^ Q(x,y) -> T(x,y)]

– There exist a person x which satisfies the following: x runs faster than y and x is older than y implies x talks louder than y

Implication

J(x) = x studies hard N(x) = x likes baseball R(x,y) = x swims faster than y \A x [J(x) ^ N(x) -> R(x,y)]

– For every person x the following holds: x study hard and x like baseball implies x does not swim faster than y

Exercise

Write FOL Statements. Everyone plays football or study. X is taller than Y if he runs faster than y. X can study AI or SE only after he has

studied C++. Mercedes and BMW cars are costly

than Toyota.