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A Default-Logic Framework for Legal Reasoning in Multiagent Systems. Vern R. Walker Hofstra University School of Law AAAI Fall Symposium, 2006 Interaction and Emergent Phenomena in Societies of Agents. The logical structure of law emerges from:.

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a default logic framework for legal reasoning in multiagent systems

A Default-Logic Framework for Legal Reasoningin Multiagent Systems

Vern R. Walker

Hofstra University School of Law

AAAI Fall Symposium, 2006

Interaction and Emergent Phenomena in Societies of Agents

the logical structure of law emerges from
The logical structure of lawemerges from:

The great multiplicity of jurisdictions, courts, and cases, and over time

The rule of law:

  • Similar cases to be decided similarly
  • Each case to be decided on its particular evidence
  • Each case to be decided through reasoned decision-making
  • Maximize transparency of reasoning
factfinding in law always balances
Factfinding in law always balances:
  • The epistemic objective: to increase the accuracyof findings of fact that are warranted by the available evidence


  • Non-epistemic objectives, e.g. –
    • Protecting public health
    • Deterring criminal activity
    • Increasing governmental efficiency
law has evolved a logic with three major components
Law has evolved a logicwith three major components:
  • Rule-Based Reasoning (creates uniformity, predictability, and transparency)
  • Evidence Evaluation (creates flexibility in applying the rules)
  • Process-constrained Decision-Making (creates uniformity, constrains discretion, promotes evolution)
the default logic framework
The “Default-Logic Framework”:

Automation (e.g., Legal

ApprenticeTM Software)

Default-Logic Frameworkrepresents

the rules, assertions, reasoning, …

Legal texts(statutes, regulations, decisions,

reports, transcripts, …) containing natural,

legal, scientific, or other specialized language.

i rule based reasoning
I. Rule-Based Reasoning

Modeled in Default-Logic Framework:

  • Conditional propositions (“if …, then …”)
  • Three-valued logic –

True / Undecided / False

  • Three truth-functional connectives –

Conjunction (“AND”)

Disjunction (“OR”)

Defeater (“UNLESS”)

Implication Trees Capture Legal Rules: e.g., the rules for Compensation underthe National Vaccine Injury Compensation Program
video screen cam of making an implication tree
Video (screen cam) ofMaking an Implication Tree
  • Using the Apprentice Decision ModelerTM
  • Which Employs a Microsoft VisioTM User Interface

Play Video 1

ii evidence evaluation
II. Evidence Evaluation

The General Challenge in Law:

  • Applying RulestoParticular Cases
  • Utilizing a GreatVariety of Evidence
    • Lay witness testimony
    • Expert witness testimony
    • Documents
    • Test results, medical records, etc.
  • Leaving Flexibility to the Discretion of theFactfinder
  • Sharing Decision-Making with Judge
ii evidence evaluation10
II. Evidence Evaluation

Modeled in Default-Logic Framework:

  • Evidentiary AssertionshavingMany-Valued Plausibility-Values
  • Plausibility Schemas Organize Evidentiary Assertions into Default Patterns of Reasoning
  • Numerous Plausibility Connectives
Five-Valued Scale


Probably True


Probably False


Seven-Valued Scale

Highly Plausible

Very Plausible

Slightly Plausible


Slightly Implausible

Very Implausible

Highly Implausible

Evidentiary Assertionsare propositions that (e.g.) either are a witness’s testimony or describe other kinds of evidence.

They have plausibility-values, e.g.:


Plausibility Schemasare logical patterns of default reasoning,which can be used in a particularcase to prove the issues identified by the legal rules (implication tree).

They employplausibility connectivesthat operate on theplausibility-valuesofevidentiary assertions, e.g.:

Generalized Conjunction (“MIN”)

Generalized Disjunction (“MAX”)

Strong Defeater (“REBUT”)

Weak Defeater (“UNDERCUT”)

for example the statistical syllogism plausibility schema
For example, the Statistical-Syllogism Plausibility Schema

IF (1) A particular individual is in category A.

(2) Most members of category A are also in category B.

(3) The members of category A adequately represent that individual with respect to being in B.

THEN,that individual is probablyalso in category B.

for example
For example,

John is a member of AAAI.

Most AAAI members are over age 15.

AAAI members adequately represent John with respect to age.

Therefore, John is probably over age 15.

The Statistical-Syllogism Schema Modeled in Legal ApprenticeTM , as applied to the Vaccine Injury Act
analyzing the reasoning in particular cases
Analyzing the Reasoning in Particular Cases

Apprentice Decision ModelerTM

  • Implication Trees(Legal Rules)
  • Plausibility Schemas(Default Logic)
  • OtherConcepts andStructures(Concepts of parties, evidence, etc.)

Legal ApprenticeTM

Environment for modeling particular cases (assigning values to subjects, selecting schemas for evidence, etc.)

Case Analyses / Reports


Illustration: modeled on Huber v. Sec. of HHS, 22 Cl.Ct. 255 (1991), a compensation case under the National Childhood Vaccine Injury Act of 1986

Petitioner was 5½-year-old boy

Received DPT shot at 4 months

Suffered seizures within days

Developed serious mental disability

Preexisting condition: tuberous sclerosis

assign values to subjects
Subjects within Implication Trees (Rules):

“the petitioner” = Adam B.

“the vaccination” = the DPT shot on Oct. 5, 2005

“the injury” = the life-long serious mental disabilities

Subjects within Plausibility Schemas:

“category A” = the category of people who have tuberous sclerosis and suffer seizures before age 2

“category B” = the category of people who have life-long serious mental disabilities

Assign Values to Subjects:
the completed schema attached to a terminal proposition of the implication tree for the vaccine act
The completed schema attached to a terminal proposition of the implication tree for the Vaccine Act
iii process constrained decision making
III. Process-Constrained Decision-Making
  • Procedural Rules and Decisions
    • Motions to dismiss
    • Motion for summary judgment
    • Directed verdict
  • Evidentiary Rules and Decisions
    • Admissibility of evidence
    • Legal sufficiency of evidence
    • Standards of proof (eg, preponderance)
iii process constrained decision making22
III. Process-Constrained Decision-Making

Modeled in Default-Logic Framework:

  • No new logical objects or structures
  • Legal rules captured by implication trees
  • Evidentiary assertions apply the rules to the particular case
emergence of new rules and rules about rules
Emergence of New Rules,and Rules about Rules
  • Many process decisions areabout adopting, maintaining, or rescinding rules of law –

that is, about theshapeof theimplication trees

  • Important area of research:

Modeling thepolicy-based reasoningof courtsabout rules

emergence of new plausibility schemas
Emergence of NewPlausibility Schemas
  • Many process decisions are about how areasonable factfinder goesaboutevaluating evidence –

e.g., deciding whether proffered evidence is minimally reliable, or deciding whether a pattern of reasoning is minimally plausible

  • Important area of research:

Developing new plausibility schemas

some conclusions
Some Conclusions
  • Law is a strategic area for studyingreasoning in multiagent, problem-oriented systems
    • Numerous complex, important cases
    • Reasoningextensive,well-documented
    • Integrates rules, evidence, and policies
    • Integrates non-expert and expert evidence and reasoning
conclusions cont
Conclusions, cont.
  • Law coordinates many agents working on different aspects of extremely complex cases
    • Legislatures and regulators
    • Judges and regulators
    • Experts and non-experts
    • Rule-makers and factfinders
  • Law evolves its own rules, policies, schemas, and logic over time –

and does so under (because of ?) the rule of law.