View
228
Download
3
Category
Tags:
Preview:
Citation preview
28-05-2007 | 1
› 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
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.
28-05-2007 | 3
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
28-05-2007 | 4
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.
28-05-2007 | 5
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.
28-05-2007 | 6
Different explanations
Event1
Event3Event2
Explanandum
28-05-2007 | 7
Different explanations
Event1
Event3Event2
Explanandum
28-05-2007 | 8
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.
28-05-2007 | 9
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”
28-05-2007 | 10
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
28-05-2007 | 11
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
28-05-2007 | 12
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
28-05-2007 | 13
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
28-05-2007 | 14
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.
28-05-2007 | 15
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.
28-05-2007 | 16
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.
28-05-2007 | 17
Example: giving explanations
› p1: Explain ({H is found}, {H robs supermarket} T1)
H is found
H hides in a moat
H fleesH robs
supermarket
28-05-2007 | 18
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
28-05-2007 | 19
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
28-05-2007 | 20
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
28-05-2007 | 21
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
28-05-2007 | 22
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
28-05-2007 | 23
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
28-05-2007 | 24
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
28-05-2007 | 25
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.
28-05-2007 | 26
Thank you for your attention
Recommended