28-05-2007 | 1
Investigating stories in a formal
dialogue game
› Floris Bex / Centre for Law and ICT
› Henry Prakken / Centre for Law and ICT
Dept. of ICS, Utrecht University
28-05-2007 | 2
Introduction
› Logical framework for analysing and reasoning with
evidence and stories in criminal cases.
› Limitation: provides a static viewpoint.
› Formal dialogue game to model the dynamics of
developing and refining an analysis of a case.
• Analysts build and refine stories (explanations)
and support them with evidence.
• Determine the best story in an adversarial setting.
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Contents of this talk
› Summary of the framework for evidential reasoning
with stories and arguments.
› A dialogue game for the analysis of evidential stories
and arguments.
› Example dialogue.
› Conclusion
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Two approaches to evidential reasoning
› Story-based approach
• Construct and compare stories about what
happened in a case.
• Modelled as abductive inference to the best
explanation (IBE).
› (Wigmorean) argument graph approach.
• Construct argument graphs from sources of
evidence to conclusion.
• Modelled with formal argumentation theory.
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Abductive inference to the best explanation
› Stories are modelled as causal networks.
› Given:
• a causal theory T consisting of causal rules of the
form event1 C event2.
• explananda F (facts to be explained).
› Hypothesize a set of causes H such that H  T
logically implies F (“explains F”).
› Compare different hypothesis according to some
criteria.
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Different explanations
Event1
Explanandum
Event2
Event3
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Different explanations
Event1
Explanandum
Event2
Event3
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Evidential arguments
› Arguments are constructed using input (evidence)
and evidential generalizations of the form P E Q.
› Arguments have a tree structure.
› An argument can be rebut or undercut by another
argument.
› An argument can be justified, overruled or defensible.
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Arguments
› Attacking arguments
John did not
shoot Peter
John shot peter
Witness says
“P” E P
Witness 2 says
”John did not
shoot Peter”
John says
Witness 1 says
”Rijkbloem shot my
”John shot Peter”
husband!”
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Arguments
› Attacking arguments
John shot peter
Witness 1 is
not trustworthy
John says
Witness 1 says
”Rijkbloem shot my
”John shot Peter”
husband!”
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Combining the theories
› The stories are modelled as causal networks
• Different stories = different explanations
› Sources of evidence are connected to the stories using
evidential arguments.
› Explanations are compared by how many sources of
evidence are covered:
• An explanation S covers a piece of evidence P if
there is a (non-overruled) argument from P to an
event in S
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The dialogue game
› Game between two players.
› Players build a model that contains explanations
supported by arguments.
› Elements of the dialogue game:
• Communication language (speech acts)
• Commitment rules
• Protocol
• Turntaking and winning
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Communication language
› Argue AR
• The speaker states an argument AR
› Explain (E, S)
• The speaker provides an explanation S for E
› Concede / retract p
• The speaker concedes or retracts p
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Protocol
› Legality of moves: a move must be a sensible
operation on the evidential framework, e.g.:
› Arguments may be stated:
• to attack other arguments
• to attack explanations
• to increase evidential support
› Explanations may be given for propositions.
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Turntaking and winning
› Adversarial setting: each player must try to advance
and support his own explanation.
› Current winner: player who is committed to the
explanation with the best evidential coverage.
› Players must try to become the current winner by
giving explanations, supporting and attacking
explanations.
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Example: the Haaknat case
› A supermarket is robbed and the masked robbers flee.
› Police conduct a search operation in a park near the
supermarket, hoping to find the robber.
› Haaknat was found hiding in a moat in the park and the police,
believing that Haaknat was the robber, apprehended him.
› Haaknat, however, argued that he was hiding in the moat
because earlier that day, he had an argument with a man called
Benny over some money.
› According to Haaknat, Benny drew a knife so Haaknat fled and
hid himself in the moat where the police found him.
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Example: giving explanations
› p1: Explain ({H is found}, {H robs supermarket}  T1)
H robs
supermarket
H flees
H hides
in a moat
H is
found
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Example: giving explanations
› p1: Explain ({H is found}, {H robs supermarket}  T1)
› p2: Explain ({H is found}, {argument between H and B}  T2)
H robs
supermarket
Argument
between H and B
H flees
H hides
in a moat
H is
found
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Example: supporting explanations with evidence
› p2: argue H testified that he had an argument with B
H robs
supermarket
Argument
between H and B
H flees
H hides
in a moat
H is
found
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Example: supporting explanations with evidence
› p2: argue AR1
H robs
supermarket
H flees
H hides
in a moat
Argument
between H and B
ge1: Witness says “P” E P
Haaknat says: “I had
an argument with B”
H is
found
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Example: attacking supporting arguments
› p1: Haaknat is a suspect and suspects do not make reliable
witnesses so ge1
H robs
supermarket
Argument
between H and B
H is a suspect
AR1
H flees
H hides
in a moat
H is
found
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Example: expanding and supporting explanations
› p1: Explain ({H robs supermarket}, {H is from S }  T3)
H is from
Suriname
H robs
supermarket
Argument
between H and B
H flees
H hides
in a moat
H is
found
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Example: expanding and supporting explanations
› p1: Explain ({H robs supermarket}, {H is from S }  T3)
› p1: Argue I have evidence that R is from Suriname
H is from
Suriname
H robs
supermarket
Argument
between H and B
Evidence
H flees
H hides
in a moat
H is
found
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Example: attacking explanations
› p2: Argue your causal generalization is based on prejudice
Prejudiced
H is from
Suriname
H robs
supermarket
Argument
between H and B
Evidence
H flees
H hides
in a moat
H is
found
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Conclusions
› Dynamic dialogue game for analysing stories and
evidence.
› Find the best explanation in an adversarial setting.
› Players jointly build a model.
› Combination of enquiry and persuasion dialogue.
› Game can provide guidelines for discussions.
› Theory can serve as basis for system AVERs.
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Thank you for your attention