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Lecture 2: Computational Semantics

The document discusses computational semantics, focusing on the representation and analysis of meaning in linguistic expressions using formal structures such as first-order logic and event representations. It outlines the requirements of meaning representations, key concepts like predicates and quantifiers, and techniques for semantic analysis, including syntax-driven approaches and corpus-based methods. Additionally, it addresses challenges such as ambiguity and underspecification, while highlighting the importance of understanding the relationship between syntax and meaning.

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Seman&c  Analysis  in  Language  Technology   http://stp.lingfil.uu.se/~santinim/sais/2014/sais_2014.htm
 
 Computa(onal  Seman(cs     Marina  San(ni   san$nim@stp.lingfil.uu.se     Department  of  Linguis(cs  and  Philology   Uppsala  University,  Uppsala,  Sweden     Autumn  2014    Lecture  2:  Computational  Semantics 1
Outline   •  Formal  Representa(ons  and  Computa(onal   approaches   –  The  Seman(cs  of  First-­‐Order  Logic   –  Event  Representa(ons   –  Descrip(on  Logics  &  the  Web  Ontology  Language   –  Syntax-­‐Driven  Seman(c  Analysis:  Composi(onality   •  Corpus-­‐based  approaches   –  Latent  Seman&c  Analysis   –  Topic  models   –  Distribu&onal  Seman&cs…   Lecture  2:  Computational  Semantics 2
Generally  speaking,  seman(cs  and  meaning…   In  linguis(cs…   •  Seman&cs  is  the  study  of  meaning   •  Meaning  is  the  core  of  human  communica(on.  It  is   the  msg  that  we  want  to  convey  (explicity  or   implicitly)   •  Meaning  representa&ons  are  formal  structures   •  Meaning  representa&on  languages  are  frameworks   that  speficy  the  syntax  and  seman(cs  of  these   representa(ons   Lecture  2:  Computational  Semantics 3
(Computa(onal)  Seman(cs  vs   Pragma(cs   •  Roughly,  seman(cs  is  the  meaning  that  can  be   deduced  directly  from  an  expression,  with  no   extra-­‐linguis(c  informa(on.     – cf:  ”the  sun  is  rising”  vs  ”the  bus”   •  Computa(onal  Seman(cs  focuses  not  only  on   the  abstract  accounts  of  meanings,  but  also  in   a  concrete  formaliza(ons  that  can  support   implementa&on   Lecture  2:  Computational  Semantics 4
Seman(c  Analysis…   …  is  the  process  that  we  use  to     – create  representa(ons  of  meaning   – assign  them  to  linguis(c  inputs   Lecture  2:  Computational  Semantics 5
WHAT  IS  NEEDED  IN  A  MEANING   REPRESENTATION?   Ch  17   Lecture  2:  Computational  Semantics 6
The  Representa(on  of  Meaning   •  Meaning  of  linguis(c  expressions  can  be  captured  in   formal  structures  that  we  call  meaning   representa&ons.   •  What  we  need  are  representa&on  that  bridge  the  gap   from  linguis&c  inputs  to  the  non  linguis&c  knowledge  of   the  world     •  It  requires  access  to  the  representa&ons  that  link  the   linguis&c  elements  involved  in  the  task  to  the  non-­‐ linguisitc  ’knowledge  of  the  world’  needed  to  perform   the  task.     Lecture  2:  Computational  Semantics 7
Seman(c  processing…   ”Learning  to  use  a  new  piece  of  soWware  by   reading  a  manual”     – knowledge  about  current  computers   – similar  soWware  applica(ons   – knowledge  about  users  in  general     Lecture  2:  Computational  Semantics 8
Requirements   •  The  basic  requirements  that  a  meaning   respresenta(on  must  fulfill:   – Verifiability   – Ambiguity   – Inference   – Expressiveness   Lecture  2:  Computational  Semantics 9
First-­‐Order  Logic   •  FOL  is  a  computa(onally  tractable  approach  to   the  representa(on  of  knowledge  that  sa(sfies   many  of  the  previous  requirements,  namely:   – Verifiability   – Inference   – Expressiveness   Lecture  2:  Computational  Semantics 10
FOL  (Wikipedia)   http://en.wikipedia.org/wiki/First-order_logic   •  First-­‐order  logic  is  a  formal  system  used  in   mathema(cs,  philosophy,  linguis(cs,  and   computer  science.     •  It  is  also  known  as:   –   first-­‐order  predicate  calculus     – the  lower  predicate  calculus   – quan&fica&on  theory   – predicate  logic   – etc.     Lecture  2:  Computational  Semantics 11
Why  ”first-­‐order”?   Lecture  2:  Computational  Semantics 12 There  are  more   powerful  forms  of   logic,  but  first-­‐‑ order  logic  is   adequate  for  most   everyday   reasoning.  
FOL   •  First-­‐order  logic  is  symbolized  reasoning  in   which  each  sentence,  or  statement,  is  broken   down  into  a  subject  and  a  predicate.     •  The  predicate  modifies  or  defines  the   proper(es  of  the  subject.     •  In  first-­‐order  logic,  a  predicate  can  only  refer   to  a  single  subject.   Lecture  2:  Computational  Semantics 13
But…  undecidable  (some(mes)   •  The  Incompleteness  Theorem  ,  proven  in   1930,  demonstrates  that  first-­‐order  logic  is  in   general  undecidable.     •  That  means  there  exist  statements  in  this  logic   form  that,  under  certain  condi(ons,  cannot  be   proven  either  true  or  false.   •  Ex:  can’t  solve  the  Hal(ng  Problem   Lecture  2:  Computational  Semantics 14
Hal(ng  Problem   •  In  1936  Alan  Turing  proved  that  it's  not  possible  to  decide  whether   an  arbitrary  program  will  eventually  halt,  or  run  forever.     •  The  official  defini(on  of  the  problem  is  to  write  a  program  (actually,   a  Turing  Machine*)  that  accepts  as  parameters  a  program  and  its   parameters.  That  program  needs  to  decide,  in  finite  (me,  whether   that  program  will  ever  halt  running  these  parameters.   •  The  hal(ng  problem  is  a  cornerstone  problem  in  computer  science.   It  is  used  mainly  as  a  way  to  prove  a  given  task  is  impossible,  by   showing  that  solving  that  task  will  allow  one  to  solve  the  hal(ng   problem.   *A  Turing  machine  is  a  hypothe(cal  device  that  manipulates  symbols   according  to  a  table  of  rules.  Despite  its  simplicity,  a  Turing  machine   can  be  adapted  to  simulate  the  logic  of  any  computer  algorithm,     Lecture  2:  Computational  Semantics 15
Representa(on   •  A  sentence  in  first-­‐order  logic  is  wrifen  in  the   form  Px  or  P(x),  where  P  is  the  predicate  and  x   is  the  subject,  represented  as  a  variable.     •  Complete  sentences  are  logically  combined   and  manipulated  according  to  the  same  rules   as  those  used  in  Boolean  algebra.   Lecture  2:  Computational  Semantics 16
FOL’s  machinery   •  Terms:     – Constants   – Func(ons   – Variables   •  Logical  connec(ves   •  Quan(fiers   •  Lambda  nota(on   Lecture  2:  Computational  Semantics 17
The  Seman(cs  of  FOL   •  Truth  table   •  Inference   Lecture  2:  Computational  Semantics 18
Predicates  and  terms   •  John  is  a  sailor                sailor(j)   •  In  FOL  we  can  represent  the  informa(on   conveyed  by  NL  entences  sta(ng  that  an  object  is   a  member  of  a  certain  set  by  means  of  a   predicate  such  as  ”sailor”  (deno(ng  a  set  of   object),  and  a  term  such  as  J,  deno(ng  John.     •  The  atomic  formula  sailor(j)  expresses  the   statement.   Lecture  2:  Computational  Semantics 19
Arity   •  Using  predicates  of  higher  arity,  we  can  also   assign  a  seman(c  interpreta(on  to  sentences   sta(ng  that  certain  objects  stand  in  certain   rela(on:   •  John  likes  Mary          like(j,m)   Lecture  2:  Computational  Semantics 20
Universal  quan(fier:  ∀   •  The  seman(c  interpreta(on  of  sentences  asser(ng   that  a  set  is  included  in  another  can  be  expressed   by  means  of  a  universal  quan(fier  ∀   Dogs  are  mammals          ∀xdogxàmammals(x)! Lecture  2:  Computational  Semantics 21
Existen(al  quan(fier:  Ǝ   •  The  existen(al  quan(fier  Ǝ  can  be  used  to   capture  the  informa(on  that  a  certain  set  is   not  empty,  as  epressed  by  the  sentence:   I  have  a  car          Ǝxcar(x)∧own(spkr,x)! Lecture  2:  Computational  Semantics 22
3  Connec(ves:  ∧∨¬   John  and  Mary  are  happy        happy(j)  ∧  happy(m)     John  is  not  married        ¬married(j)         In  certain  applica(ons,  represen(ng  this  info  is  all  we   need  (eg.  enquiry  system  for  train  transporta(on:  a   person  travelling  from  sta(on  a)  to  sta(on  b)       Lecture  2:  Computational  Semantics 23
λ    nota(on  &  λ  reduc(on   •  It  is  a  way  to  ”abstract”  from  FOL  formulae   •  λ  followed  by  one  or  more  variables,  followed   by  a  FOL  formula  that  makes  use  of  these   variables.     •  Basically:  manipula(on  and  aggrega(on  of   variables.     Lecture  2:  Computational  Semantics 24
Example:  lambda  expressions   •  λx.λy.Near(x,y)  =  something  near  something  else     •  λx.λy.Near(x,y)(uppsala)   –  Reduc(on:  λy.Near(uppsala,y)     •  λy.Near(uppsala,y)  (stockholm)   –  Reduc(on:  Near(uppsala,stockholm)     •  More:  Sec(ons  17.3.3  and  18.3;  see  also hfps://files.nyu.edu/cb125/public/Lambda/     Lecture  2:  Computational  Semantics 25
Proof  Theory   •  What  makes  FOL  a  logic  is  that  it  also  includes   a  specifica(on  of  the  valid  conclusions  that   can  be  derived  from  the  info.     a)  All  trains  depar(ng  from  Stockholm  and   arriving  at  Gävle  stop  at  Uppsala   b)  Train  531  departs  from  S  and  arrives  at  G.   c)  Train  531  stops  at  U   Lecture  2:  Computational  Semantics 26
Inference  rules   1.  ∀x(train(x)∧depart(x,S)arrive(x, G) à stop(x, U)! 2.  train(t531)∧depart(t531),S)∧arrive(t531,G)! 3.  stop(t531,U)! •  An  inference  rule  consists  of  a  set  of  statements   called  premises  and  a  statement  called  conclusion.   The  inference  rule  is  a  claim  that  if  all  premises  are   true,  then  the  conclusion  is  true.     Lecture  2:  Computational  Semantics 27
Ex:  Modus  ponens  =  if-­‐then  reasoning   •  It  is  an  example  of  a  valid  inference  rule:   – If  P  is  the  case,  and  P  à  Q  is  the  case,  than  Q  is   the  case.   Lecture  2:  Computational  Semantics 28
Cf.  Proposi(onal  logic  (wikipedia)   http://en.wikipedia.org/wiki/Aristotelian_logic   •  Syllogism  and  inference:   –  Men  are  mortal  =  A   –  Socrates  is  a  man  =  B   –  Socrates  is  mortal  =  C     Proposi(onal  logic  (also  called  senten(al  logic)  is  the  logic  the  includes  sentence  lefers   (A,B,C)  and  logical  connec(ves,  but  not  quan$fiers.     The  seman(cs  of  proposi(onal  logic  uses  truth  assignments  to  the  lefers  to  determine   whether  a  compound  proposi(onal  sentence  is  true.     The  syllogism  is  an  inference  in  which  one  proposi(on  (the  "conclusion")  follows  of   necessity  from  two  others  (the  "premises").  A  proposi(on  may  be  universal  or  par(cular,   and  it  may  be  affirma(ve  or  nega(ve.       Syntac(cally,  first-­‐order  logic  has  the  same  connec(ves  as  proposi(onal  logic,  but  it  also   has  variables  for  individual  objects,  quan(fiers,  symbols  for  func(ons,  and  symbols  for   rela(ons.  The  seman(cs  include  a  domain  of  discourse  for  the  variables  and  quan(fiers  to   range  over,  along  with  interpreta(ons  of  the  rela(on  and  func(on  symbols.   Lecture  2:  Computational  Semantics 29
Many  Logic-­‐s   •  logic  of  sentences  (proposi(onal  logic),     •  logic  of  objects  (predicate  logic),     •  logic  involving  uncertain(es,     •  logic  dealing  with  fuzziness,     •  temporal  logic  etc.   Lecture  2:  Computational  Semantics 30
Prac(cal  use  Of  Modus  Ponens     •  Forward  chaining   –  Top-­‐down:  As  soon  as  a  new  fact  is  added  to  the   knowledge  base,  all  applicable  rules  are  found  and   applied,  each  esul(ng  n  the  addi(on  of  new  facts  to   then  KB.  Drawback:  facts  that  will  never  be  needed   are  deduced  and  stored   •  Backward  chaining:     –  Bofom  up:  run  in  reverse  to  prove  specific   proposi(ons  are  true  (à  PROLOG).   •  Both  incomplete:   –  Ie,  there  valid  inferences  that  cannot  be  found  by   systems  that  use  these  methods  alone.     Lecture  2:  Computational  Semantics 31
State  and  Event  Representa(ons   •  States  and  events   – States  are  condi(ons,  or  proper(es,  that  remain   unchanged  over  a  period  of  (me   – Events  denote  changes  in  some  state  of  affairs   Lecture  2:  Computational  Semantics 32
Predicates   •  Predicates  in  FOL  have  fixed  arity:  they  take  a  fixed   number  of  arguments  –  predicates  have  a  fixed   arity   Lecture  2:  Computational  Semantics 33
Possible  solu(on   •  event  variables  à  (neo)  Davidsonian  event   representa(on   Ǝe eating(e) ∧ eater(e, speaker)∧ eaten(e,turkey sandwich) ∧ meal(e,lunch) ∧ location(e,desk)∧time(e,tuesday)# •  No  need  to  specify  a  fixed  number  of  arguments   •  The  event  itself  is  a  single  argument.     •  Everything  else  is  captured  by  addi(onal  predica(on   Lecture  2:  Computational  Semantics 34
Descrip(on  Logics   •  DLs  refer  to  a  family  of  logical  approaches  that  corrispond  to   different  subsets  of  FOL.     •  We  can  use  DLs  to  model  an  applica(on  domain.  The  focus  is  then   on:   –  Representa(on  of  knowledge  about  categories   –  The  set  of  categories  in  an  applica(on  domain  is  called  terminology   –  The  terminology  is  arranged  in  a  hierachical  organiza(on  called   ontology,  which  capture  superset  &  subset  rela(ons  among  categoires/ concepts.     –  In  order  to  specify  a  hierachical  structure,  we  can  use  subsump$on   rela(ons  betw  the  appropriate  concepts  in  a  terminiology     –  Subsump$on  is  a  form  of  inference.  Determines  whether  a  suprset/ subset  rela(on  (based  on  the  fact  asserted  in  a  terminology)  exists  betw   two  concepts.   Lecture  2:  Computational  Semantics 35
OWL  and  the  Seman(c  Web   •  A  Descrip(on  Logic  roughly  similar  to  the  previous   example  is  used  in  the  Web  Ontology  Language  (OWL).     •  OWL  is  a  language  used  for  the  develoment  of   ontologies  that  should  encapsulate  the  knowledge  in   the  development  of  the  Seman(c  Web   •  The  Seman(c  Web  is  the  effort  to  formally  specify  the   seman(cs  of  the  contents  of  the  web  .   à  lect  9   Lecture  2:  Computational  Semantics 36
Seman(c  web  (wikipedia)   hfp://en.wikipedia.org/wiki/Seman(c_Web     •  The  Seman(c  Web  is  a  collabora(ve  movement  led  by   interna(onal  standards  body  the  World  Wide  Web   Consor(um  (W3C).     •  By  encouraging  the  inclusion  of  seman(c  content  in  web   pages,  the  Seman(c  Web  aims  at  conver(ng  the  current   web,  dominated  by  unstructured  and  semi-­‐structured   documents  into  a  "web  of  data".     •  Web  3.0   –  Tim  Berners-­‐Lee  has  described  the  seman(c  web  as  a   component  of  "Web  3.0".   –  "Seman(c  Web"  is  some(mes  used  as  a  synonym  for  "Web   3.0",  though  each  term's  defini(on  varies.   Lecture  2:  Computational  Semantics 37
TECHNIQUES  FOR  ASSIGNING   MEANINGS  TO  LINGUISTIC  INPUT   J&M  -­‐  Ch  18              see  also  Saeed,  Ch  10:  Formal  se   Lecture  2:  Computational  Semantics 38
Syntax-­‐Driven  Seman(c  Analysis   •  :  Meaning  representa(ons  are  assigned  to   sentences  on  the  basis  of  knowledge  taken   from  the  lexicon  and  grammar   Lecture  2:  Computational  Semantics 39
Principle  of  Composi(onality   •  PoC:  the  meaning  of  a  sentence  can  be   constructed  from  the  meaning  of  its  parts.     •  Watch  out!  the  meaning  of  a  sentence  is  not   based  only  on  the  words  that  make  it  up,  but  also   on  the  ordering  and  grouping  of  words  and  on   the  rela(ons  among  the  words  in  the  sentence.     •  Basically,  the  meaning  of  a  sentence  is  par(ally   based  on  its  syntac(c  structure.     Lecture  2:  Computational  Semantics 40
The  rule-­‐to-­‐rule  hypothesis   •  we  do  not  define  languages  by  enumera(ng   the  meanings  that  are  permifed.     •  But  we  define  a  finite  set  of  devices  that   generate  the  correct  meaning  for  the  context.     •  These  devices  are  based  on  grammar  rules   and  lexical  entries.   Lecture  2:  Computational  Semantics 41
Two  constrained  approaches   1.  The  first  is  based  on  FOL  and  lambda-­‐ nota(on.   2.  The  second  is  based  on  feature-­‐structure  and   unifica(on   Lecture  2:  Computational  Semantics 42
1:  FOL   •  Every  restaurant  has  a  menu,  2  meanings:   – All  restaurants  have  a  menu   – There  is  a  menu  in  the  world  and  all  the  restarrants   share  it   Lecture  2:  Computational  Semantics 43
1.  Quan(fier  scope  ambiguity   •  Expressions  containing  quan(fiers  can  create   ambiguity  even  if  there  is  no  syntac(c,  lexical   or  analphoric  ambiguity.     Lecture  2:  Computational  Semantics 44
Underspecifica(on  and  storage   •  The  restaurant  fills  the  haver  role  and  the  menu  fills  the   had  role.     •  it  remain  agnos(c  about  the  placement  of  the   quan(fies   Lecture  2:  Computational  Semantics 45 We  use  λ-­‐expressions    and  a  store.     The  quan(fied  expressions  are  in   the  form  of  λ-­‐‑expressions  thant   can  be  combined  with  the  core   representaton  in  the  right  way.   We  have  access  to  the  quan(fier  via   the  index.     See  Section  18.3
Drawback   •  fail  to  generated  all  the  possible  ambiguous   representatons  arising  from  the  quan(fier   scope  ambigui(es.       àunderspecifica(on  =  Including  all  possible   readings  without  enumera(ng  them     (probabili(es?)       Lecture  2:  Computational  Semantics 46
Idioms  and  Composi(onality  (Sect  18.6)   •  What  kind  of  meaning  representa(on  do  we   need  for  idioms?   •  The  (p  of  the  iceberg  à  flexible   – iceberg’s  (p   – (p  of  an  iceberg   – (p  of  a  rather  large  iceberg     – (p  of  a  larger  iceberg     •  Kick  the  bucket  à  crystallized   Lecture  2:  Computational  Semantics 47
CORPUS-­‐BASED  APPROACHES  AND   MACHINE  LEARNING   Lecture  2:  Computational  Semantics 48
Latent  Seman(c  Analysis   (wikipedia)   http://en.wikipedia.org/wiki/Latent_semantic_analysis   •  Latent  seman(c  analysis  (LSA)  is  a  technique  of  analyzing  rela(onships   between  a  set  of  documents  and  the  terms  they  contain  by  producing  a  set   of  concepts  related  to  the  documents  and  terms.     •  LSA  assumes  that  words  that  are  close  in  meaning  will  occur  in  similar   pieces  of  text.     •  A  matrix  containing  word  counts  per  paragraph  is  constructed  from  a  large   piece  of  text  and  a  mathema(cal  technique  called  singular  value   decomposi(on  (SVD)  is  used  to  reduce  the  number  of  rows  while   preserving  the  similarity  structure  among  columns.     •  Words  are  then  compared  .  Values  close  to  1  represent  very  similar  words   while  values  close  to  0  represent  very  dissimilar  words.”   Applica$ons  and  Limita$ons…  Lecture  2:  Computational  Semantics 49
Topic  Models   (wikipedia)   http://en.wikipedia.org/wiki/Topic_model   ”  a  topic  model  is  a  type  of  sta(s(cal  model  for  discovering  the   abstract  "topics"  that  occur  in  a  collec(on  of  documents.  Intui(vely,   given  that  a  document  is  about  a  par(cular  topic,  one  would  expect   par(cular  words  to  appear  in  the  document  more  or  less  frequently:   "dog"  and  "bone"  will  appear  more  oWen  in  documents  about  dogs,   "cat"  and  "meow"  will  appear  in  documents  about  cats,  and  "the"  and   "is"  will  appear  equally  in  both.  A  document  typically  concerns   mul(ple  topics  in  different  propor(ons;  thus,  in  a  document  that  is   10%  about  cats  and  90%  about  dogs,  there  would  probably  be  about  9   (mes  more  dog  words  than  cat  words.  A  topic  model  captures  this   intui(on  in  a  mathema(cal  framework,  which  allows  examining  a  set   of  documents  and  discovering,  based  on  the  sta(s(cs  of  the  words  in   each,  what  the  topics  might  be  and  what  each  document's  balance  of   topics  is.”     Latent  Dirilecht  Alloca$on  (LDA)   Lecture  2:  Computational  Semantics 50
Distribu(onal  Seman(cs   (wikipedia)   http://en.wikipedia.org/wiki/Distributional_semantics   ”Distribu$onal  seman$cs  is  a  research  area  that  develops  and   studies  theories  and  methods  for  quan(fying  and  categorizing   seman(c  similari(es  between  linguis(c  items  based  on  their   distribu(onal  proper(es  in  large  samples  of  language  data.  The   basic  idea  of  distribu(onal  seman(cs  can  be  summed  up  in  the   so-­‐called  Distribu(onal  hypothesis:  linguis&c  items  with  similar   distribu&ons  have  similar  meanings”       Applica$ons  and  Limita$ons…     Lecture  2:  Computational  Semantics 51
SemEval   (wikipedia)   http://en.wikipedia.org/wiki/SemEval   •  SemEval  (Seman(c  Evalua(on)  is  an  ongoing  series  of  evalua(ons  of   computa(onal  seman(c  analysis  systems;  it  evolved  from  the  Senseval   word  sense  evalua(on  series.  The  evalua(ons  are  intended  to  explore  the   nature  of  meaning  in  language.  While  meaning  is  intui(ve  to  humans,   transferring  those  intui(ons  to  computa(onal  analysis  has  proved   elusive.This  series  of  evalua(ons  is  providing  a  mechanism  to  characterize   in  more  precise  terms  exactly  what  is  necessary  to  compute  in  meaning.   As  such,  the  evalua(ons  provide  an  emergent  mechanism  to  iden(fy  the   problems  and  solu(ons  for  computa(ons  with  meaning.  These  exercises   have  evolved  to  ar(culate  more  of  the  dimensions  that  are  involved  in  our   use  of  language.  They  began  with  apparently  simple  afempts  to  iden(fy   word  senses  computa(onally.  They  have  evolved  to  inves(gate  the   interrela(onships  among  the  elements  in  a  sentence  (e.g.,  seman(c  role   labeling),  rela(ons  between  sentences  (e.g.,  coreference),  and  the  nature   of  what  we  are  saying  (seman(c  rela(ons  and  sen(ment  analysis).   Lecture  2:  Computational  Semantics 52
In  this  course…   •  We  are  not  going  to  focus  on   formalisms  or  on  corpus-­‐based   approaches  to  seman(cs.  We  will   focus  some  specific  aspects  of   meaning  that  are  useful  for  NLP   and  IR  applica(ons,  namely…   Lecture  2:  Computational  Semantics 53
The  End       Lecture  2:  Computational  Semantics 54