The logic of propositions requires a formula: Predicate Argument'

1

• Introduction
• - The logic of propositions requires a formula
  Predicate (Argument).
• - Speech-at Proposition Event .
• CP IP VP
  
•   - Formula also consists of modifiers.

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• - We have a typology of semantic constituent
  classes ( THING, STATE OF AFFAIRS, EVENT,
  SITUATION, ACTION)
• John arrived ACTION.
• Mary adores the colour greenSTATE.

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Definitions

• . Predicates
• - A predicate a relational expression which
  combines with an argument.
• - A predicate can refer to a verb which requires
  a number of arguments, depending on what a verb
  subcategorizes.

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• - At least three classes of verbs are
  distinguished
• Intransitive verbs one argument.
• Transitive verbs two arguments.
• Ditransitive verbs three arguments.

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Examples

• smile NP1.
• meet NP1 NP2.
• give NP1 NP2 NP3.
• NP1 NP2 PP.

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• Arguments
• An argument refers to any constituent that is
  semantically required by some predicate to
  combine with that predicate.

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Examples

• The boy killed the bird.
• The boy killed.
• John gave Mary a present.
• gave Mary a present.

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Characteristics

• - Arguments are semantically differentiated
  according to their semantic role.

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Semantic roles

• ACTOR the doer of an Action.
• The wind blew down the tree.
• ? The wind blew down the tree on purpose.
• The earthquake destroyed the whole city.
• ? The earthquake destroyed the whole city
  on
• purpose.

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• - When the ACTOR has an INTENTION to ACT, she or
  he AGENT.

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• - AGENT the one who intentionally initiates the
  action expressed by the predicate.
• The dog chased the cat.
• The dog chased the cat on purpose.

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A Problem

• John left the room.
• John AGENT, or
• John ACTOR.

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Solution

• The context is obligatory to determine
• the intentionality or unintentionality of
• Johnaction.

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• - PATIENT the person or thing undergoing the
  action expressed by the predicate
• The doctor examined the patient. 

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• THEME the person or thing moved by the action
  expressed by the predicate.
• John gave Mary a book.
• John gave a book to Mary.

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• - EXPERIENCER the entity that experiences some
  (psychological) state expressed by the the
  predicate

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• John fears snakes STATE
• John fears snakes on purpose.
• John EXPERIENCER.
• Snakes EXPERIENTIAL TRIGGER.

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• - GOAL the entity towards which the activity
  expressed by the predicate is directed.
• John gave the present to Mary

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• SOURCE the entity from which something is moved
  as a result of the activity expressed by the
  predicate.
• Charlie brought the lamp from Bill.
• John rolled the rock from the dump to the
  house.

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• . Adjuncts
• - Adjuncts can be divided into two categories
• - Obligatory adjuncts arguments.
• He dresses awfully.
• He dresses.
• John treated Mary badly.
• John treated Mary.

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• - Optional adjuncts constituents that provide
  extra information.
• The plane arrived on time.
• The planed arrived.

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Some approaches to the predicate-argument
relation.

• Ordered-Argument system
• Thematic roles system

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• Ordered-Argument system
• - It is inherited from formal predicate logic.
• - A verb is translated as a predicate which
  requires a fixed number of arguments to form a
  formula.
• Every formula has a truth value.
• - Conventional.

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• Example
• gives (x, y, z).
• gives (j, m, p).

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• Thematic roles system
• - It makes use of semantic roles like Agent,
  Patient, Sourcein the semantic interpretation of
  predicates and arguments.

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• Example
• (predicate give), (agent, x), (theme, y),
• (goal, z)(semantically indexed).

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From the conventional to the semantic content

• Approaches to thematic roles
• . Ordered-Argument system
• . Neo-Davidsonian system

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• Thematic roles from an ordered point of view
• - A thematic role is a cluster of entailments
  shared by arguments of the verb.

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Definition

• Given an n-place predicate d and a particular
  argument xi, the individual thematic role
• (d, i) is the set of all properties ? such
  that the entailment
• d(x1, ...,xi ...,...,xn)? ?(xi)
• holds.

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Example

• x builds y.
• - If its truth value is true, then the
  builder-role entails that there must be a
  buildee-role.

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Definition

• Thematic role type
• Given a set T of pairs lt d, id gt where d is an
• n-place predicate and id the index of one of its
  
• arguments (possibly i for each verb), a thematic
  role type Y is the intersection of all the
  individual thematic roles determined by T.

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Conditions on L- thematic roles

• Completeness
• Distinction
• Independence

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• . Completeness
• every individual thematic role contains
  some thematic role type (every argument position
  of every verb is assigned an L-thematic role
  type).
• Distinction
• All argument positions of the same verb
  are assigned different L-themtic role.

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• Independence
• The properties in an L- thematic role type
  must be characterizable independently of the
  relations (denoted by natural language verbs)
  that entail them.

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Adverbs analysis as a Davidsons key motivation
for introducing events

• - Adverbs are predicates of events, allowing a
  very simple account of how they are semantically
  integrated into the clause.
• a- Mary kissed John quickly
• b- e kiss(m, j, e) quick (e, C)

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Dowtyanalysis

• Not only modifiers but also the arguments of
  verbs are actually predicates of events.
• Every argument is added to the verb by means of
  conjunction.

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Example

• ?e kissing (e) Agent(e, m) Theme(e, j)
• there is a kissing and it is by Mary and it is
  of John .

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Equivalence between the two approaches

• ?x ?y ?z give(x, y, z) ?
• ?e giving (e) occur(e) Source(x, e)
  Theme(y, e) Goal(z, e).

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• The Neo-Davidsonian advantages
• -It does not impose a certain restriction on
  arguments.
• - Semantic coherence.

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• Example
• ?e giving(e) Source(j, e) Theme(the-book, e)
  Goal(m, e).
• ?egiving(e) Source(j, e) Theme(the-book,
  e).
• ?e giving(e) Source(j, e) Goal(m, e).
• ?e giving(e) .

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• Another advantage concerns nouns.
• a- The gift of a book from john to mary will
  surprise Bill.
• b- The gift of a book to mary will surprise Bill.
• c- The gift from john to mary will surprise Bill.
• d- The gift will surprise Bill.

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Disadvantages

• It can not capture structures which show
  transitivity and intransitivity.

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Conclusion

• a- The ordered-argument method tends to associate
  verbs with their subcategorized
• arguments.
• b- The Neo-Davidsonian method of arguments tends
  to associate verbs with their adjuncts, and nouns
  denoting events with their arguments.

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Carlsonanalysis

• Carlson seems to support the Neo-Davidsonian.
• This applies only to verbs like eat.

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• - Counter-example
• a- John shaved someone.
• b- John shaved.