LING%581:%Advanced%Computaonal% Linguiscssandiway/ling581-15/lecture11.pdf · –...

LING 581: Advanced Computa7onal Linguis7cs

Lecture Notes April 16th

Administrivia

•  Factoid Ques-on Answering homework – did you submit your simula.on?

Seman7cs

•  New topic! – We want computers to be able to understand sentences,

– model the world, – compute meaning, truth values, entailments etc.

Meaning •  What is a meaning and how do we represent it?

–  difficult to pin down precisely for computers –  even difficult for humans some.mes…

•  Example: word dog –  by reference to other words

•  Merriam-‐Webster: a highly variable domes.c mammal (Canis familiaris) closely related to the gray wolf

–  transla7on •  犬 (inu, Japanese) = 狗 (gou, Chinese) = “dog” (English)

–  Computer: •  meaning è formal concept (or thought or idea) •  “dog” maps to DOG •  <word> maps to <concept> •  need to provide a concept for every meaningful piece of language?

Understanding •  Suppose we write a computer program to compute the meaning of

sentences •  Ques7on: does it understand sentences? •  How do you know? •  Ask ques7ons?

•  Turing test: –  converse with a human, convince human the computer is a human

•  Searle’s Chinese room experiment (adapted) –  suppose we have a Perl/Python/Prolog program capable of processing

Chinese, and we “run” the program manually –  i.e. we carry out the instruc.ons of the program –  do we understand Chinese?

•  Weak AI / Strong AI

Truth Condi7ons and Values

•  What is the meaning of a sentence anyway? •  What is Meaning? (Portner 2005)

•  Example: the circle is inside the square – We can draw a picture of scenarios for which the statement is true and the statement is false

•  Proposi7on expressed by a sentence is its truth-‐condi7ons –  “under what condi7ons a sentence is true” –  i.e. sets of possible worlds (aka situa7ons) –  truth-‐condi.ons different from truth-‐value


•  Example: –  The circle is inside the square and the circle is dark – What is the meaning of and here? –  and = set intersec7on (of scenarios) –  [The circle is inside the square] and [the circle is dark]

•  Example: – Mary is a student and a baseball fan –  and = set intersec7on (of ???) – Mary is [a student] and [a baseball fan]


•  Example: – Mary and John bought a book – Does and = set intersec7on? – Are Mary and John sets anyway?

–  [Mary] and [John] bought a book

– Set intersec7on = ∅ – how about “and = set union” then?


•  Example: – The square is bigger than the circle – The circle is smaller than the square

– Are they synonymous? – Are they contradictory? –  Is there an entailment rela7onship? – Are they tautologies?

More examples •  1. Does sleep entail snore?

A.  He is sleeping entails He is snoring B.  He is snoring entails He is sleeping

•  2. Does snore presuppose sleep? •  3. What does “when did you stop bea.ng your wife?” presuppose?

•  3. Given the statement “All crows are black”, give an example of a sentence expressing a tautology involving this statement? –  Stmt or nega7on Stmt

Proposi7onal Logic

•  Recall the dis7nc7on between truth condi7ons and truth values …

•  Possible world or situa7on: – we can create a possible world in Prolog by asser7ng (posi7ve) facts into its database

– Prolog use the closed world assump7on •  i.e. things not explicity stated to be true are assumed to be false

Proposi7onal Logic Cheat sheet •  Star7ng SWI Prolog from Terminal/Shell:

–  swipl (if in PATH) –  /opt/local/bin/swipl (default install loca7on on my mac)

^D (control-‐D) or halt. to quit

Proposi7onal Logic Cheat sheet •  Viewing the database:

–  listing.

•  Assert (and delete) facts at the command line directly using predicates: –  assert(fact).–  retract(fact).

•  Put facts into a file and load file –  [filename]. (assumed to have extension .pl) –  (or via pull-‐down menu in Windows)

•  Proposi7ons: –  named beginning with a lower case lejer (not number, not star7ng with capital lejer or

underscore: variable – no variables in proposi7onal logic), examples:

–  assert(p). (makes p true in this situa7on) –  p. (asks Prolog if p true in this situa7on) –  dynamic q. (registers proposi7on q, prevents error message)

Proposi7onal Logic

•  Example:

Note: meta-‐level predicates like dynamic and assertevaluate to true if they succeed

Proposi7onal Logic •  Proposi7ons can be combined using logical connec7ves and

operators –  Conjunc7on p , q. –  Disjunc7on p ; q. –  Nega7on \+ p.

•  Not directly implemented in Prolog –  Implica7on p -‐> q. (IS NOT THIS!!!)

can’t add p, q. to the database can only query it

Use parentheses ( ) to restrict/clarify scope

needs both p and q to be true, see next slide

Proposi7onal Logic

•  Help: –  ?- help(->).–  true.

takes a very long 7me for this window to pop up … it uses the X11 Window system, which may or may not exist on your system

IF -‐> THEN ; ELSE is a programming construct

Proposi7onal Logic •  Also not implemented

–  Logical equality p = q.

Proposi7onal Logic •  Help:

Not quite the right documenta7on page = is unifiability in Prolog

Proposi7onal Logic •  Prolog exercise:

–  evaluate formula below for different truth values of A and B

From wikipedia

Proposi7onal Logic

•  How to demonstrate a proposi7onal formula is a tautology?

•  One answer: exhaus7vely enumerate a truth table

hjp://en.wikipedia.org/wiki/Truth_table

Proposi7onal Logic •  Example:

(A , B) ; (\+ A) ; (\+ B) (A , B) ; (\+ A) ; (\+ B)

T T T T

T F T F

F T F T

F F F F

(A , B) ; (\+ A) ; (\+ B)

T T T T T

T F F T F

F F T F T

F F F F F

(A , B) ; (\+ A) ; (\+ B)

T T T F T F T

T F F F T T F

F F T T F F T

F F F T F T F

(A , B) ; (\+ A) ; (\+ B)

T T T F T F F T

T F F F T T T F

F F T T F T F T

F F F T F T T F

(A , B) ; (\+ A) ; (\+ B)

T T T F T F F T

T F F F T T T F

F F T T F T F T

F F F T F T T F

(A , B) ; (\+ A) ; (\+ B)

T T T T F T F F T

T F F T F T T T F

F F T T T F T F T

F F F T T F T T F

table has 2n rows, where n is the number of proposi7onal elements complexity: exponen7al in n

Proposi7onal Logic

•  Other connec7ves (are non-‐primi7ve)

Proposi7onal Logic

•  Other connec7ves (are non-‐primi7ve)

aka p ↔ q

•  From 1st and 4th line of truth table, we can easily deduce how to simulate p ↔ q in Prolog using , ; and \+

Proposi7onal Logic

hjp://en.wikipedia.org/wiki/Tautology_(logic)

Let’s prove the law of contraposi7on

Proposi7onal Logic

•  Prove both sides of De Morgan’s Laws:

Note: De Morgan’s laws tell us we can do without one of conjunc7on or disjunc7on. Why?

Proposi7onal Logic

•  It’s easy to write a short program in Prolog to automate all this …

Program: plogic.pl

Proposi7onal Logic •  Example using try/2:

It's a tautology! true under all possible condi7ons

Proposi7onal Logic •  We can get a bit fancier, support -‐> and <-‐>

Program: plogic2.pl

Proposi7onal Logic •  We can get even fancier; eliminate having to supply the

proposi7onal variables

Program: plogic3.pl

Truth table enumera7on

•  Parsing the formula:

11. \+ X converts to \+ A if (subformula) X converts to A 12. X,Y converts to A,B if X converts to A and Y converts to B 13. X;Y converts to A;B if X converts to A and Y converts to B 14. X-‐>Y converts to \+A;B if X converts to A and Y converts to B 15. X<-‐>Y converts to (A,B) ; (\+A,\+B) if X converts to A and Y converts to B 16. X converts to X and add X to the list of proposi7onal variables if it isn’t already in the list

Proposi7onal Logic Program: plogic3.pl

Seman7c Grammars •  Use slides from course –  LING 324 – Introduc-on to Seman-cs –  Simon Frasier University, Prof. F.J. Pelle7er –  hjp://www.sfu.ca/~jeffpell/Ling324/ypSlides4.pdf

•  Difference is we’re computa.onal linguists… so we’re going to implement the slides

•  •  We’ll do the syntax part this lecture, and the seman7cs next 7me

Syntax

ypSlides4.pdf Slide 3

Syntax •  We already know how to build Prolog grammars •  See –  hjp://www.swi-‐prolog.org/pldoc/doc_for?object=sec7on(2,'4.12',swi('/doc/Manual/DCG.html'))

for the execu7ve summary

Syntax

•  Class exercise

Syntax •  Step 1: let’s build the simplest possible Prolog grammar for this


Simplest possible grammar Excluding (2b) for the 7me being g1.pl

Simplest possible grammar

Examples (3), (4) and (5) from two slides back

Syntax •  Step 2: let’s add the parse tree component to our grammar …

Recall: grammar rules can have extra arguments (1)  Parse tree (2)  Implement agreement etc.

Syntax Note: on handling lez recursion in Prolog grammar rules •  techniques:

1.  use a bojom-‐up parser 2.  rewrite grammar (lez recursive -‐> right recursive) 3.  or use lookahead (today’s lecture)

lookahead is a dummy nonterminal that does not contribute to the parse, it is a “guard” that prevents rule from firing unless appropriate lookahead succeeds if it can find a conjunc7on in the input and marks it (so it can’t find it twice)

Grammar: version 2 g2.pl

Grammar: version 2

Grammar: version 2

Examples (3), (4) and (5) again from slide 9

Grammar: version 2

Examples (6) and (7) from slide 9

Seman7cs

•  We want to obtain a seman7c parse for our sentences that we can “run” (i.e. evaluate) against the Prolog database (i.e. situa7on or possible world).

•  So the seman7c parse should be valid Prolog code (that we can call)

•  We’ll need (built-‐in) member/2 and setof/3 defined in the following 2 slides (a quick review)

setof/3 •  See

–  hjp://www.swi-‐prolog.org/pldoc/doc_for?object=sec7on(2,'4.29',swi('/doc/Manual/allsolu7ons.html'))

•  SWI Prolog built-‐in:

setof/3

•  Example:

member/2 •  See –  hjp://www.swi-‐prolog.org/pldoc/man?predicate=member%2F2

Seman7cs


Seman7cs: Implementa7on

•  Desired implementa7on:

The extra argument returns a Prolog query that can be evaluated against the database

Note: we are bypassing the (explicit) construc7on of the syntax tree Imagine if the Penn Treebank was labeled using a seman.c representa.on

Seman7cs: Implementa7on •  Let’s write the seman7c grammar to handle “Jack is hungry”

–  first, let’s introduce a bit of nota7on (lambda calculus) –  λ = func7on –  λx.x+1 denotes a func7on that takes an argument x and computes

value x+1 •  (a period separates the argument from the func.on body)

–  (λx.x+1)(5) means apply 5 to the lambda func7on •  subs7tute 5 in place of x and evaluate •  answer = 6


setof(X,hungry(X),S) jack

setof(X,hungry(X),S), member(jack,S)

Syntax:

Seman7cs: Implementa7on •  Seman7c grammar:


•  More examples of computa7on: ypSlides4.pdf Slide 10


•  More examples of computa7on:

Seman7cs



•  Scope of nega7on: wide or narrow

narrow

wide

Grammar: version 3 g3.pl

Grammar: version 3

Evalua7on

•  Check our computer implementa7on on…


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