Discourse Understanding with
Discourse Representation Theory
and Belief Augmented Frames
Colin Tan,
Department of Computer Science,
School of Computing,
National University of Singapore.
Belief Augmented Frames
Motivation
• 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
slot’s value is changed, removed etc.
Belief Augmented Frames
Motivation
• In the original definition of frames, slotvalue pairs are “definite”.
• One improvement is to introduce
uncertainties into these relations.
Belief Augmented Frames
Motivation
• Statistical representations are not always ideal:
– If we are p% certain that a fact is true, this doesn’t
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
Belief Augmented Frames
Motivation
• 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.
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.
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
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)
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
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.
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.
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)] ===> [u3=u1
u4=u2
beats(u3, u4)]]
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=> [u3=u1
u4=u2
love(u3, u4)]]
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.
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.
From DRS to BAF
• Alternatively, if person C says that Pedro
doesn’t 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.
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.
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|.
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 today’s 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.
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(action:stole, object:purse),
purse(action:stolenby, subject:cat)?
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 counterintuitive:
– E.g. plsf < Tf , when Tf , Ff > 0.5
Difficulties
• The range for the sum of Tf ,andFf falls in
[0, 2] instead of [0, 1]. This is again
counter-intuitive.
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.