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› Floris Bex / Centre for Law and ICT

›Henry Prakken / Centre for Law and ICT Dept. of ICS, Utrecht University

Investigating stories in a formal dialogue game

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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

Event3Event2

Explanandum

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Different explanations

Event1

Event3Event2

Explanandum

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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 says ”Rijkbloem shot my

husband!”

John shot peter

Witness 1 says ”John shot Peter”Witness 1 says

”John shot Peter”

Witness says “P” E P

Witness 2 says ”John did not shoot Peter”

John did not shoot Peter

Witness 1 says ”John shot Peter”

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Arguments

John says ”Rijkbloem shot my

husband!”

John shot peter

Witness 1 says ”John shot Peter”Witness 1 says

”John shot Peter”

Witness 1 is not trustworthy

John shot peter

› Attacking arguments

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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 is found

H hides in a moat

H fleesH robs

supermarket

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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 is found

H hides in a moat

H fleesH robs

supermarket

Argument between H and B

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Example: supporting explanations with evidence› p2: argue H testified that he had an argument

with B

H is found

H hides in a moat

H fleesH robs

supermarket

Argument between H and B

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Example: supporting explanations with evidence› p2: argue AR1

H is found

H hides in a moat

H fleesH robs

supermarket

Argument between H and B

Haaknat says: “I had an argument with B”

ge1: Witness says “P” E P

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Example: attacking supporting arguments› p1: Haaknat is a suspect and suspects do not make

reliable witnesses so ge1

H is found

H hides in a moat

H fleesH robs

supermarket

Argument between H and B

AR1

H is a suspect

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Example: expanding and supporting explanations› p1: Explain ({H robs supermarket}, {H is from S } T3)

H is found

H hides in a moat

H fleesH robs

supermarket

Argument between H and B

H is fromSuriname

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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 found

H hides in a moat

H fleesH robs

supermarket

Argument between H and B

H is fromSuriname

Evidence

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Example: attacking explanations

› p2: Argue your causal generalization is based on prejudice

H is found

H hides in a moat

H fleesH robs

supermarket

Argument between H and B

H is fromSuriname

Evidence

Prejudiced

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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