Discourse Understanding with Discourse Representation Theory and Belief Augmented Frames

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Discourse Understanding with Discourse
Representation Theory and Belief Augmented Frames

• Colin Tan,
• Department of Computer Science,
• School of Computing,
• National University of Singapore.

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Belief Augmented FramesMotivation

• Frames
• Flexible, intuitive way of representing
  knowledge.
• Frames represent an entity or a concept
• Frames consist of slots with values
• Represents relations between current frame and
  other frames.
• Slots have events attached to them
• Can invoke procedures (daemons) whenever a
  slots value is changed, removed etc.

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Belief Augmented FramesMotivation

• In the original definition of frames, slot-value
  pairs are definite.
• One improvement is to introduce uncertainties
  into these relations.

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Belief Augmented FramesMotivation

• Statistical representations are not always ideal
• If we are p certain that a fact is true, this
  doesnt mean that we are 1-p certain that it is
  false.
• Various uncertainty reasoning methods introduced
  to address this
• Dempster-Schafer Theory
• Transferrable Belief Model
• Probabilistic Argumentation Systems

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Belief Augmented FramesMotivation

• By combining uncertainty measures with frames
• Uncertainties in slot-value pair assignments
  provide frames with greater expressiveness and
  reasoning ability.
• Frames offer a neat intuitive structure for
  reasoning uncertain relations.

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Modeling Uncertainty in Belief Augmented Frames

• Uncertainty not only on slot-value pair
  assignments, but also on the existence of the
  concept/object represented by the frame.
• The belief mass ?Tf is called the Supporting
  Mass, and it is the degree of support that the
  fact f is true.
• Likewise ?Ff is the Refuting Mass, and it is the
  degree of support that the fact f is false.

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Modeling Uncertainty in Belief Augmented Frames

• In general
• 0 ? ?Tf , ?Ff ? 1
• ?Tf is fully independent of ?Ff
• ?Tf ?Ff ? 1
• The Degree of Inclination Dif is defined as
• Dif ?Tf - ?Ff
• The Plausibility plf is defined as
• Plf 1 - ?Ff

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Combining Belief Masses

• Fuzzy-logic style min-max functions are used to
  combine belief masses from different facts.
• Given two facts P and Q
• Conjunctions
• ?TP?Q min(?TP, ?TQ)
• ?FP?Q max(?FP, ?FQ)

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Combining Belief Masses

• Given two facts P and Q
• Disjunctions
• ?TP?Q max(?TP, ?TQ)
• ?FP ? Q min(?FP, ?FQ)
• Negation
• ?T?P ?FP
• ?F?P ?TP

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BAF-Logic

• The three combination rules allow us to perform
  reasoning using the Supporting and Refuting
  masses.
• This reasoning system is called BAF-Logic, or
  just BAFL.

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Reasoning Rules underBAF-Logic

• Expressions in BAF-Logic obey the following rules
  unconditionally
• Commutativity and Associativity
• Absorption
• Contradiction and Tautology
• De-Morgans Theorem
• Negation Elimination

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Reasoning Rules underBAF-Logic

• The following rules hold if DI of component
  facts exceeds 0.5
• ?-introduction
• ?-elimination
• Modus Ponens
• Modus Tolens

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Discourse Representation Structures

• Discourse Representation Theory provides the
  techniques and structures for resolving important
  discourse processing issues like anaphoric and
  ellipses references.
• The main structure in DRT is the Discourse
  Representation Structure, or DRS.

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Example

• An example DRS representing Pedro owns a donkey
  is shown below
• u1 u2 pedro(u1)
• donkey(u2)
• owns(u1, u2)
• The symbols u1 and u2 are known as referent
  markers.

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Embedded DRSs

• Embedded DRSs are used to model more complex
  relations
• Conditionals If Pedro owns a donkey he will beat
  it.
• u1 u2 pedro(u1)
• donkey(u2)
• owns(u1, u2) u3u1
• 
  u4u2
• 
  beats(u3, u4)

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Embedded DRSs

• Some, Few, Most, All etc are similarly modeled.
  E.g.
• Some men who own donkeys love them.
• u1 u2 men(u1)
• donkey(u2)
• own(u1, u2) some u3u1
• 
  u4u2
• 
  love(u3, u4)

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From DRS to BAF

• Conversion from DRS to BAF is trivial
• All nouns and objects are inserted as new frames
  in the BAF
• New frames for Pedro(u1) and Donkey(u2) are
  created.
• All relations between nouns and objects in the
  DRS are modeled slot-value pairs in the BAF. E.g.
• beats(u1, u2)
• u1 is resolved to Pedro, u2 is resolved to
  donkey, a slot beats is created in Pedro and the
  frame for donkey is assigned to it.

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From DRS to BAF

• Uncertainties for slot-value assignments
• For simple relations (e.g. Pedro owns a donkey)
• ?Towns(pedro, donkey) ?
• ?Fowns(pedro, donkey) 1- ?
• Here ? is our degree of belief in the reliability
  of the source that told us that Pedro owns a
  donkey.

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From DRS to BAF

• Alternatively, if person C says that Pedro
  doesnt own a donkey, then
• ?Towns(pedro, donkey) ?
• ?Fowns(pedro, donkey) ?
• This example illustrates the expressive power of
  making ?T and ?F separate and fully independent.

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From DRS to BAF

• Fuzzy relations like some, most, etc. can be
  represented in BAF by using fuzzy-logic style
  membership functions.
• E.g. Some boys beat their donkeys
• Let S be the set of boys who beat their donkeys.
• ?Tbeat(boys, donkeys) f(S)
• ?Fbeat(boys, donkeys) 1 - ?Tbeat(boys, donkeys)
  
• Here f(.) is a monotonically increasing function
  definied in the range 0, 1, similar to the
  fuzzy-logic S function.

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From DRS to BAF

• Other fuzzy notions can also be similarly
  expressed
• All boys beat their donkeys
• Let S be the set of boys who beat their donkeys,
  and let D be the set of boys who own donkeys.
  Then
• ?Tbeat(boys, donkeys) ?(S D)
• ?Fbeat(boys, donkeys) 1 - ?Tbeat(boys, donkeys)
  
• Here ? is a proximity function, defined on 0,
  1, that increases as S approaches D.

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Applications

• Several applications of BAFs are currently being
  developed
• Q A system
• Digests newswire articles and answers questions.
• Most direct application of the topics in todays
  talk.
• Text Classification System
• Uses abstraction feature of BAFs to learn the
  features of document classes.
• Use these features to classify unseen documents.
• Results are better than Naïve Bayes.

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Difficulties

• Semantics of slots is ill-defined
• There is no fixed way to use the slots to
  represent relations between frames.
• This complicates the modeling of real-world
  English sentences. E.g.
• The black cat stole the purse.
• Should this be modeled as stole(subject cat,
  object purse), cat(actionstole, objectpurse),
  purse(actionstolenby, subjectcat)?

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Difficulties

• Many ways to derive a-priori Supporting and
  Refuting masses.
• Some ways might be better than others.
• Separation of Supporting and Refuting masses
  introduces additional problems that can make
  modeling awkward and counter-intuitive
• E.g. plsf 0.5

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Difficulties

• The range for the sum of ?Tf ,and?Ff falls in
  0, 2 instead of 0, 1. This is again
  counter-intuitive.

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Future Work

• More work to be done in incorporating linguistic
  hedges like very and somewhat.
• A model for measuring the quality of the
  knowledge in the BAF knowledge base should be
  developed.