Semantic Theory

Lexical semantics
1. 1st attempt
  1. davidson's problem
    1. entailments not natural
  2. davidson' proposal/ Event semantics
    1. for event verb
      1. introduce e
      2. predicate(e, _ ,_ ) \and adjuncts
    2. model structure
      1. introduce event space
      2. (Individual universal, event universal, interpretation function)
      3. variable assignment function
      4. for different domains
    3. added values
      1. natural representation of adjuncts
      2. natural and uniform interpretation event verbs and nomial event predicates
      3. uniform treatment of NPs and infinitive constructions as verb complements
      4. bill saw an elephant
      5. bill saw an accident
      6. bill saw the children play
      7. intuitive semantic constructions for adjuncts
      8. it rains at midnight
      9. at midnight
      10. adjuncts modify event predicate
      11. uniform treatment of noun modifiers
      12. the murder in the park
      13. the fountain in the park
      14. the plausible integration of tense
    4. tense
      1. classical tense logic
      2. representations
      3. with tense operators
      4. p
      5. Pwalk(john)
      6. f
      7. Fwalk(john)
      8. tense logical model structure
      9. M= <U, T, <, V>
      10. U \union T= \empty
      11. < a linear ordering on T
      12. V value assignment function
      13. interpretation
      14. temporal event structure
      15. M = (U, E, T, < , t_u, tl, V)
      16. U, E, T mutually disjoint
      17. < linear ordering on T
      18. t_u \in T
      19. utterance time
      20. tl
      21. function from E to interval of T
      22. V interpretation function
      23. order of events
      24. precedence of events
      25. e < e'
      26. for all t \in tl(e), t' in \tl(e')
      27. t < t'
      28. overlapping events
      29. e \circle e'
      30. iff
      31. tl(e) \conjunt tl(e') \neq \empty
      32. stative vs non-staive
      33. stative
      34. know
      35. believe
      36. have
      37. desire
      38. love
      39. non-stative
      40. kick
      41. run
      42. walk
      43. build a house
      44. Summary
      45. with extra argument e!
2. event semantics
  1. stative vs event
    1. linguistic distinction
      1. progressive form
      2. john is running
      3. john is reciting a poem
      4. john is knowing the answer
      5. simplest present
      6. mary runs
      7. has the habit of running
      8. john recites peoms
      9. has the habit of reciting poems
      10. john knows the answer
      11. manner adverbials
      12. John ran carefully
      13. John carefully recited the poem
      14. John carefully knew the answer
    2. conclusion
      1. verb semantics using events
      2. natural
      3. however
      4. not all verbs
      5. event-expressing verbs do not form a homogeneous semantic class
  2. differences
    1. different distribution of duration adverbials
      1. e.g.
      2. john painted a picture in an hour
      3. john walked in an hour
      4. it rained in an hour
      5. john walked for an hour
      6. it rained for hour
      7. john painted a picture for an hour
      8. it took john an hour to paint a picture
      9. it took john an hour to walk
    2. different inferential properties
      1. john walked from 8am to 11 am
      2. john walked from 9 to 10 am
      3. it rained from 8 am to 11 am
      4. it rained from 9 to 10 am
      5. john painted a picture from 8am to 11 am
      6. not!
      7. john painted a picture from 9 to 10 am
      8. john is working in Saarbrucken
      9. John has worked in Saarbrucken
      10. it is raining in Saarbrucken
      11. it has rained in Saarbrucken
      12. john is painting a picture
      13. not
      14. john has painted a picture
      15. john stopped walking
      16. john walked
      17. it stopped raining
      18. it rained
      19. john stopped painting a picture
      20. not
      21. john painted a picture
  3. aspectual verb classes(relation to time)
    1. states
      1. know
      2. believe
      3. own
      4. love
      5. resemble
    2. eventualities
      1. processes/activities
      2. run
      3. walk
      4. swim
      5. work
      6. sleep
      7. rain
      8. (Proper) Events
      9. e.g.
      10. paint?
      11. still not homogeneous!!!
      12. accomplishments
      13. (succeed in doing somehing)
      14. achievements
    3. vendler's classification
      1. duration?
      2. bound?
      3. Problem remained
      4. what is the essential ontological difference
      5. compositional treatment?
  4. NOUNs
    1. plural NPs
      1. collective predicates
      2. Bill and Mary met
      3. not
      4. Bill met
      5. The students gathered, John is a student
      6. not
      7. John gathered
      8. e.g.
      9. meet
      10. gather
      11. unite
      12. agree
      13. distributive predicates
      14. Bill and Mary worked
      15. Bill worked
      16. The students worked, John is a student
      17. John worked
      18. modeling
      19. idea
      20. structured universe
      21. entities
      22. atomic
      23. sum/group
      24. plural
      25. group
      26. lattice
      27. partial order
      28. reflective
      29. transitive
      30. antisymmetric
      31. closed under
      32. join
      33. meet
      34. differences
      35. collecitve
      36. V_M(F) \in U\A
      37. distributive
      38. distributivity
      39. closure under summation
      40. mixed
      41. not distributive
      42. but closed under summation
      43. e.g.
      44. carry a piano
      45. solve the exercise
      46. language
      47. summation operator
      48. +
      49. At
      50. atom
      51. (proper) individual part
      52. number specific predicates
      53. interpretation
      54. +
      55. <|
      56. individual constants
      57. atoms
      58. sums
      59. number-specific predicate
    2. mass nouns(3)
      1. vs plurals
      2. similarities
      3. closed under summation
      4. combine with cardinalities
      5. 5 students
      6. 5 liters of water
      7. share grammatical patterns
      8. differences
      9. divisive
      10. denotations cannot be reduced to atomic individuals
      11. modeling
      12. another sort of entities
      13. portions of matter
      14. non-atomic and dense join semi-lattice
      15. language
      16. add
      17. +_m
      18. <|_m
      19. materialization function
      20. m (type <e, e>)
      21. object-matter relation
      22. h
      23. map atomic and pluralic individuals to matter
      24. homomorphism
  5. event semantics in analogy to plural semantics
    1. idea
      1. sub-event relation
      2. join semi-lattice
      3. (U, <E, <=_e>, <, e_u, V)
      4. <
      5. asymmetric relation
      6. e_u
      7. utterance event
      8. <E, <=_e>
      9. join semi-lattice
      10. V
      11. interpretation function
    2. application
      1. scripts
    3. process event vs proper events
      1. process
      2. similar to mass
      3. cumulative
      4. divisive
      5. M = (!U, !i", !M, !m", h, !Ei, !ei" , !Em, !em", he, <, eu, V)
    4. progressive tense
3. thematic role
compositional semantics
1. first order logic(recap)
  1. describe properties and relations of individuals
  2. individuals
    1. CON
    2. VAR
    3. terms?
  3. quantification is also on individuals
  4. limitation
    1. modification
      1. good student
    2. sentence embedding verbs
    3. higher order quantification
  5. Doesn't support Compositional semantics
  6. Summary
    1. so the limitation is due the central place of INDIVIDUALS
    2. we want to also talk about properties of relations
2. aim
  1. can compute meaning from small pieces
3. Type theory
  1. richer inventory
    1. higher order relation
  2. teminology
    1. Types
      1. basic types
      2. e
      3. entities
      4. t
      5. truth-values
      6. complex types
      7. indicates how many arguments, what types the arguments must have
  3. vocabulary
    1. constants
    2. variables
    3. logical symbols
  4. syntax
    1. well formed expressions for t
      1. CON and VAR
      2. <\theta, \tau> + \theta
      3. with logic connectives
      4. with quantifiers
      5. equation
  5. semantics
    1. domain of possible denotations
      1. D_e = U
      2. D_t={0,1}
    2. characteristic functions
    3. model structure
      1. U
      2. individuals
      3. V
      4. interpretations function for CON
    4. variable assignment
    5. meaning postulates
      1. to get intended entailment relations
      2. restrictions on models
      3. constrain the possible meaning of certain words
      4. eg
      5. adjectives
      6. intersective
      7. subsective
      8. privative
    6. construction
      1. 1st version
      2. apply verb to noun
      3. problems
      4. quantifiers on NP
      5. complex NP
      6. 2nd version
      7. motivation
      8. use lambda abstraction
      9. apply NP on VP
      10. lambda operation
      11. we + lambda
      12. scope
      13. smallest WE
      14. \lambda x.
      15. widest possible scope
      16. beta reduction
      17. variable capturing
      18. due to
      19. name
      20. scope
      21. construction rules
      22. N
      23. NP
      24. DET
      25. VP
      26. TV
      27. IV
  6. type for expressions
    1. <e,t>
      1. nouns
      2. student
      3. adjectives
      4. red
      5. a meaning of type <e,t>
      6. property
      7. set
      8. unary predicate
      9. intransitive verbs
      10. verb phrases
      11. hate Mary
      12. relative clauses
    2. e
      1. proper name
      2. definite description
      3. the professor
    3. <<e,t>, t>
      1. quantification expression
      2. no one
      3. every one
    4. <<e,t>,<<e,t>,t>>
      1. determiner
  7. lambda calculus
    1. predicate
      1. the number of arguments is not specified
      2. type of arguments is not specified
    2. benefits
      1. a way to express complex properties/ sets
      2. e.g.
      3. lazy professor
      4. \lambdax . lazy(x) \and professor(x)
  8. type shifting
  9. how to create lambda formula from predicate
    1. first do lambda abstraction according to the number of place
    2. Then choose place to put the place holder for the direct object
  10. scope ambiguity
    1. reason
      1. mismatch between syntactic and semantic structure
    2. cooper storage
      1. introduction
      2. expression are assigned ordered pairs
      3. content
      4. quantifier store
      5. quantifiers
      6. either apply in situ
      7. or move to store for later application
      8. sentence node
      9. retrieval
      10. semantic representation
      11. if store is empty
      12. storing a quantifier
      13. move it upwards
Discourse Semantics
1. DRT
  1. difference with logic
    1. no quantifiers symbol
      1. depends on the context
    2. accessblity
      1. conditions can use discourse referents
      2. why important
      3. a man sleeps
      4. \exist x (M(x) \and S(x))
      5. not every man doesn't sleep
      6. \not \any (M(x) \implies \not S(x))
      7. In DRT
      8. not fully equivalent
      9. +"he snores"
      10. 1=> perfect
      11. 2=> can not refer to x
      12. can not look downwards
      13. another example
      14. "a man doesn't sleep, he is awake"
    3. not only truth condition,
      1. model embedding
    4. but also anaphoric potential
      1. DRS construction
  2. semantic representational theory
    1. while logic concerns about truth condition
  3. truth condition
    1. K is true in M iff there is a verifying embedding f of K in M such that Dom(f) = U_K
  4. construction rules
  5. translation rules
  6. DRSs
    1. simple DRSs
    2. conditional DRSs
      1. motivation
      2. donkey sentence
      3. K_1 => K_2
      4. K_1
      5. antecedent DRS
      6. K_2
      7. consequent DRS
  7. non-compositional
    1. needs structural information
2. presuppostions
  1. requirements that the context must satisfy for the utterance to be interpretable
  2. usually to top level
  3. sometimes blocked
    1. the king has a son
    2. the king's son is bald
    3. if the king has a son, the king's son is bald
      1. there is a king
      2. survive
      3. the king has a son
      4. cancelled
  4. some triggers
    1. definite noun phrases
    2. quantifiers
    3. factive verbs
      1. regret, realize
    4. implicative verbs
    5. aspect
    6. appostions, non-restrictive relative clauses
    7. it-clefts
    8. sentence particles
  5. presupposition projection
  6. presupposition filtering
    1. block projection
  7. presupposition cancellation
3. tree levels of meaning
  1. assertions
  2. presuppostions
  3. conversational implicatures
    1. cooperative principle
    2. four maxims of conversation
      1. maxim of quality
      2. don't say what you believe to be false
      3. don't say that for which you lack evidence
      4. maxim of quantity
      5. maxim of relevance
      6. maxim of manner
4. presuppositions in DRT
  1. overview
    1. anaphora with semantic content
    2. anaphora binding
      1. filtering
    3. not bound
      1. accommodated
  2. idea
    1. anaphora
      1. the cancellor decides
      2. there is a chancellor, (s)he decides
    2. \alpha DRSs
      1. definite noun phrases
      2. \alpha DRSs
      3. pronouns
      4. proper names
      5. standard
      6. \alpha
      7. both ok
      8. possessives
      9. resolve \alpha DRSs
      10. bind
      11. accormodate
      12. usually happens on the top level
  3. preference
    1. binding > accommodation
    2. binding: closest possible
    3. accommodation: highest possible
  4. constraints
    1. free variable
    2. further constraints
overview
1. truth-conditional semantics
  1. to know the meaning
  2. to know the world when the sentence is true
  3. sentence meaning = truth-conditions
2. central concepts
  1. reference and denotation
  2. Truth and truth conditions
  3. Entailment and inference
3. compositional semantics
  1. semantic construction
    1. interpretation of adjectives
      1. john is a blond piano player
      2. john is blond
      3. john is a poor piano player
      4. john is poor
  2. quantifier scope
    1. quantifier
      1. related to quantity
      2. every
      3. a lot of
      4. many
      5. ...
      6. Summary
      7. type of determiner
  3. generalized quantifiers
4. discourse semantics
  1. anaphora and ellipsis
  2. DRT
  3. presuppositions
  4. tense and temporal structure
5. lexical semantics
  1. event semantics
  2. thematic roles
  3. plurals, mass nouns, collective predicates
formal foundations
1. predicate logic
  1. Vocab
    1. Non-logical expression
      1. individual constants
      2. CON
      3. Relation constants
    2. infinite set of individual variables
      1. VAR
    3. logical connectives
    4. Brackets
  2. Syntax
    1. Terms
      1. VAR
      2. CON
    2. atomic formulas
      1. R
      2. t1=t2
    3. well-formed formulas
      1. all atomic
      2. wff + logical connectives
      3. wff + quantifier
    4. free and bound variables
      1. all related to quantifier
      2. sentence
      3. is a formula without free variables
  3. semantics
    1. interpreted with model structure and variable assignment
      1. why?
      2. model structure is something models the world
      3. we care about the world when the sentence is true
      4. it means we care about the model structure when the sentence is true
    2. model structure
      1. U_M
      2. universe
      3. non empty
      4. can be considered as where the individuals live
      5. V_M
      6. interpretation function
      7. for constants
      8. V_M(P) \subseteq U_M^n
      9. for n-place predicate symbol
      10. V_M(C) \in U_M
    3. interpretation
      1. Terms
      2. [[a]]^{M,g}
      3. V_M(a)
      4. constant
      5. g(a)
      6. variable
      7. Formulas
      8. see the slides
      9. atomic
      10. with logic connectives
      11. with quantifiers
      12. variable assignment
      13. the idea is we only care about small part the function
      14. then just record the changed thing
    4. truth
      1. true
      2. formula is true in a model structure M iff interpretation is true for all variable assignment
      3. valid
      4. true in all model structures
      5. satisfiable
      6. true in at least one model structure
      7. entails
Generalized quantifiers
1. definition
  1. a set of properties
  2. a set of sets
  3. relation between set and set
2. motivation
  1. what formal properties do quantifiers hold
  2. what natural subclasses can be distinguished
  3. which subclasses actually represent meanings of noun phrases
  4. phenomenon
    1. negative polarity items
      1. noboday saw anthing
      2. somebody saw anything
    2. there sentence
      1. there is John in the garden
    3. coordination
      1. no man and few women walked
      2. a man and few women walked
      3. how
      4. and
      5. but
      6. Subtopic 3
3. monotonicity
  1. upward
  2. downward
4. language universals
  1. monotonicity constraint
    1. simple noun phrase of any natural language express monotone quantifiers or conjunctions of monotone quantifiers
  2. simple noun phrase
    1. proper names or noun phrases
5. negation of quantifiers
  1. external negation
  2. internal negation
  3. monotonicity
    1. if upward
      1. then both negations are upward
    2. vice versa
  4. dual
  5. example
    1. Topic
6. determiners
  1. binary quantifiers
    1. monotonicity according to verbs
    2. and according to nouns
  2. interpretation
    1. can be considered as the relation between two sets
  3. persistence (according to nouns)
    1. upward
  4. antipersistence
    1. downward
  5. conservativity
    1. Q(A, B) <=> Q(A, A \and B)
    2. test
      1. all students work
      2. all students are students that work
  6. lives on
    1. Q lives on X
    2. for all Y, Y \in Q iff X \conjuct Y \in Q
  7. only
    1. not a determiner?
  8. Summary
    1. related to monotonicity
      1. first argument
      2. second argument