Reasoning in Law Leon van der Torre University of Luxembourg November 6, 2013
Leon van der Torre 路 University of Luxembourg
November 6, 2013 1/48
Leon van der Torre 路 University of Luxembourg
November 6, 2013 2/48
Three questions
1
Why do we need formal models of reasoning in law?
2
Which formal models are best for reasoning in law?
3
What are the challenges for reasoning in law?
Leon van der Torre 路 University of Luxembourg
November 6, 2013 3/48
Why do we need formal models of reasoning in law?
Leon van der Torre 路 University of Luxembourg
November 6, 2013 4/48
Why do we need formal models of reasoning in law?
Mathematization of the social sciences
Leon van der Torre 路 University of Luxembourg
November 6, 2013 4/48
Why do we need formal models of reasoning in law?
Mathematization of the social sciences Interdisciplinarity:
Leon van der Torre 路 University of Luxembourg
November 6, 2013 4/48
Why do we need formal models of reasoning in law?
Mathematization of the social sciences Interdisciplinarity: Law is hard to understand for people outside the discipline (like computer scientists)
Leon van der Torre 路 University of Luxembourg
November 6, 2013 4/48
Which formal models are best for reasoning in law?
Leon van der Torre 路 University of Luxembourg
November 6, 2013 5/48
Which formal models are best for reasoning in law?
AI&Law: ontologies, norms, argumentation, . . .
Leon van der Torre 路 University of Luxembourg
November 6, 2013 5/48
Which formal models are best for reasoning in law?
AI&Law: ontologies, norms, argumentation, . . . Logics developed in multiagent systems (MAS)
Leon van der Torre 路 University of Luxembourg
November 6, 2013 5/48
Which formal models are best for reasoning in law?
AI&Law: ontologies, norms, argumentation, . . . Logics developed in multiagent systems (MAS) Two examples (from ten logics in MAS, an ECAI12 tutorial)
Leon van der Torre 路 University of Luxembourg
November 6, 2013 5/48
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(Third edition) by Stuart Russell and Peter Norvig The leading textbook in Artificial Intelligence. Used in over 1200 universities in over 100 countries. The 25th most cited publication on Citeseer (and 2nd most cited publication of this century).
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Leon van der Torre 路 University of Luxembourg
Table of Contents [Full Contents] Preface [html] Part I Artificial Intelligence 1 Introduction 2 Intelligent Agents Part II Problem Solving 3 Solving Problems by Searching 4 Beyond Classical Search 5 Adversarial Search 6 Constraint Satisfaction Problems Part III Knowledge and Reasoning 7 Logical Agents 8 First-Order Logic 9 Inference in First-Order Logic 10 Classical Planning 11 Planning and Acting in the Real World 12 Knowledge Representation Part IV Uncertain Knowledge and Reasoning 13 Quantifying Uncertainty 14 Probabilistic Reasoning 15 Probabilistic Reasoning over Time 16 Making Simple Decisions
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Week of Oct 10
Overview of AI, Search
Assignment 1 due Oct 17
Week of Oct 17
Statistics, Uncertainty, and Bayes networks
Assignment 2 due Oct 24
Week of Oct 24
Machine Learning
Assignment 3 due Oct 31
Schedule
Week of Oct 31
Logic and Planning
Assignment 4 due Nov 7
Translators
Week of Nov 7
Markov Decision Processes and Reinforcement Learning
Assignment 5 due Nov 17
Week of Nov 14
Hidden Markov Models and Filters
MIDTERM EXAM Nov 19-21
Week of Nov 21
Adversarial and Advanced Planning
Assignment 6 due Nov 30
Week of Nov 28
Image Processing and Computer Vision
Assignment 7 due Dec 5
Week of Dec 5
Robotics and robot motion planning
Assignment 8 due Dec 12
Week of Dec 12
Natural Language Processing and Information Retrieval
FINAL EXAM Dec 16-18
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Sebastian Thrun is a Research Professor of Computer Science at derStanford Torre 路 University of Luxembourg University, a Google Fellow, a
November 6, 2013 7/48
4841 citations
An Introduction to M by Michael Wooldridge Published May 2009 by John Wiley & Sons
ISBN-10: 0470519460 ISBN-13: 978-0470519462
Table of Contents
Leon van der Torre 路 University of Luxembourg
Multiagent systems are a distributed systems, wh components are autonom furtherance of their own Multiagent Systems was became November the standard un 6, 2013 8/48
4841 citations An Introduction to MultiAgent Systems - Second Edition
Contents
An Introduction to M
Preface
by Michael Wooldridge
by Michael Wooldridge
What was left out and why Omissions and errors Part I Setting the Scene
Published May 2009
Chapter 1 Introduction 1.1 The Vision Thing
1.2 Some Views of the Field 1.2.1 Agents as a paradigm for software engineering
by John Wiley & Sons
1.2.2 Agents as a tool for understanding human societies 1.3 Frequently Asked Questions (FAQ)
Part II Intelligent Autonomous Agents Chapter 2 Intelligent Agents 2.1 Intelligent Agents
ISBN-10: 0470519460 ISBN-13: 978-0470519462
2.2 Agents and Objects
2.3 Agents and Expert Systems
2.4 Agents as Intentional Systems
2.5 Abstract Architectures for Intelligent Agents 2.6 How to Tell an Agent What to Do Chapter 3 Deductive Reasoning Agents 3.1 Agents as Theorem Provers 3.2 Agent-Oriented Programming
Multiagent systems are a distributed systems, wh components are autonom furtherance of their own Multiagent Systems was became November the standard un 6, 2013 8/48
3.3 Concurrent MetateM
Chapter 4 Practical Reasoning Agents
4.1 Practical Reasoning = Deliberation + Means-Ends Reasoning 4.2 Means--Ends Reasoning
4.3 Implementing a Practical Reasoning Agent 4.4 The Procedural Reasoning System
Chapter 5 Reactive and Hybrid Agents 5.1 Reactive Agents
5.1.1 The Subsumption Architecture 5.1.2 PENGI
5.1.3 Situated automata
Table of Contents
Leon van der Torre 路 University of Luxembourg
5.1.4 The Agent Network Architecture
5.1.5 The Limitations of Reactive Agents
455 citations
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Main Page 455 citations
new!
Table of Contents Instructional Resources Errata eBook Download
BRIEF CONTENTS
1 Distributed Constraint Satisfaction 2 Distributed Optimization 3 Introduction to Noncooperative Game Theory: Games in Normal Form 4 Computing Solution Concepts of Normal-Form Games 5 Games with Sequential Actions: Reasoning and Computing with the Extensive Fo 6 Richer Representations: Beyond the Normal and Extensive Forms 7 Learning and Teaching 8 Communication 9 Aggregating Preferences: Social Choice 10 Protocols for Strategic Agents: Mechanism Design 11 Protocols for Multiagent Resource Allocation: Auctions Multiagent Systems 12 Teams of Selfish Agents: An Introduction to Coalitional Game Theory 13 Logics of Knowledge and Belief 14 Beyond Belief: Probability, Dynamics and Intention Appendices new!
Main Page Table of Contents Instructional Resources Errata eBook Download
Algorithmic, Game-Theoretic, and Logical Foundations Yoav Shoham Stanford University Kevin Leyton-Brown University of British Columbia
Cambridge University Press, 2009 Order online:
“This is by far the best text in the field of multiagent systems, one of the fastest-growing areas in computer science.”
— Stuart Russell, of University of California at Berkeley Leon van der Torre · University Luxembourg
November 6, 2013 10/48
The ‘traditional’ view Organized around economic theories 1
Decisions, choices: knowledge level, epistemic logic, preference logic, logics for goals, action logics, agent logics
Leon van der Torre · University of Luxembourg
November 6, 2013 11/48
The ‘traditional’ view Organized around economic theories 1
Decisions, choices: knowledge level, epistemic logic, preference logic, logics for goals, action logics, agent logics
2
Processes, time, plans, BDI theory
Leon van der Torre · University of Luxembourg
November 6, 2013 11/48
The ‘traditional’ view Organized around economic theories 1
Decisions, choices: knowledge level, epistemic logic, preference logic, logics for goals, action logics, agent logics
2
Processes, time, plans, BDI theory
3
Game theory, coalition logic, strategic logics, equilibrium logics
Leon van der Torre · University of Luxembourg
November 6, 2013 11/48
The ‘traditional’ view Organized around economic theories 1
Decisions, choices: knowledge level, epistemic logic, preference logic, logics for goals, action logics, agent logics
2
Processes, time, plans, BDI theory
3
Game theory, coalition logic, strategic logics, equilibrium logics
4
Social choice, voting, aggregation, merging
Leon van der Torre ¡ University of Luxembourg
November 6, 2013 11/48
The ‘traditional’ view Organized around economic theories 1
Decisions, choices: knowledge level, epistemic logic, preference logic, logics for goals, action logics, agent logics
2
Processes, time, plans, BDI theory
3
Game theory, coalition logic, strategic logics, equilibrium logics
4
Social choice, voting, aggregation, merging
5
Mechanism design, artificial social systems, normative systems
Leon van der Torre ¡ University of Luxembourg
November 6, 2013 11/48
Example: ATL: What Agents Can Achieve
ATL: Alternating-time Temporal Logic (Alur et al. 1997) Temporal logic meets game theory Main idea: cooperation modalities
Leon van der Torre 路 University of Luxembourg
November 6, 2013 12/48
Example: ATL: What Agents Can Achieve
ATL: Alternating-time Temporal Logic (Alur et al. 1997) Temporal logic meets game theory Main idea: cooperation modalities hhAii : coalition A has a collective strategy to enforce
Leon van der Torre 路 University of Luxembourg
November 6, 2013 12/48
Syntax ' ::= p | ¬' | ' ^ ' | hhAii , ::= ' | ¬ | ^ | g | 3 | 2 |
Leon van der Torre · University of Luxembourg
U .
November 6, 2013 13/48
Syntax ' ::= p | ¬' | ' ^ ' | hhAii , ::= ' | ¬ | ^ | g | 3 | 2 |
U .
hhjamesbondii3(ski ^ ¬getBurned): “James Bond can go skiing without getting burned”
Leon van der Torre · University of Luxembourg
November 6, 2013 13/48
Syntax ' ::= p | ¬' | ' ^ ' | hhAii , ::= ' | ¬ | ^ | g | 3 | 2 |
U .
hhjamesbondii3(ski ^ ¬getBurned): “James Bond can go skiing without getting burned”
Leon van der Torre · University of Luxembourg
November 6, 2013 13/48
Syntax ' ::= p | ¬' | ' ^ ' | hhAii , ::= ' | ¬ | ^ | g | 3 | 2 |
U .
hhjamesbondii3(ski ^ ¬getBurned): “James Bond can go skiing without getting burned”
hhjamesbond, bondsgirliifun U shot: “James Bond and his girlfriend are able to have fun until someone shoots at them” Leon van der Torre · University of Luxembourg
November 6, 2013 13/48
ATL Models: Concurrent Game Structures 1
2
pos0
2
1
pos1 2
1
pos2
Leon van der Torre 路 University of Luxembourg
November 6, 2013 14/48
ATL Models: Concurrent Game Structures 1
wait,wait push,push
2
pos0
sh
,pu
sh ,w pu
2
wa it
h
1
it
us
2
Leon van der Torre 路 University of Luxembourg
wa
wait,wait push,push
it,p
pos1
sh, pu
1
pos2
pos0 wa
ait
q0
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wait,push
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November 6, 2013 14/48
Example: Robots and Carriage wait,wait push,push
pos0
h us
,w a sh
it,p wa
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pos0
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us
pu
wa
it,p
wa
wait,wait push,push
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wait,push
pos2
push,wait
Leon van der Torre 路 University of Luxembourg
q1
hh1ii2卢pos1
wait,wait push,push
pos1
November 6, 2013 15/48
Example: Robots and Carriage wait,wait push,push
pos0
h us
,w a sh
it,p wa
it
pos0
h
us
pu
wa
it,p
wa
wait,wait push,push
sh, pu
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wait,push
pos2
push,wait
Leon van der Torre 路 University of Luxembourg
q1
hh1ii2卢pos1
wait,wait push,push
pos1
November 6, 2013 15/48
Example: Robots and Carriage
q0
pos0
h us
,w a sh
it,p wa
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pu
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it,p
push
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wait,push
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push,wait
Leon van der Torre 路 University of Luxembourg
q1
hh1ii2卢pos1
wait,wait push,push wait
pos1
November 6, 2013 15/48
Example: Robots and Carriage wait wait,wait push,push
it ,wa h us
sh pu
pos0
it,p
pu
pos0 wa
wait,wait push,push
sh ,w ait wa it,p us h
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Leon van der Torre 路 University of Luxembourg
q1
hh1ii2卢pos1
wait,wait wait push,push
pos1
November 6, 2013 15/48
Example: Robots and Carriage wait wait,wait push,push
it ,wa h us
sh pu
pos0
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pu
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sh ,w ait wa it,p us h
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Leon van der Torre 路 University of Luxembourg
q1
hh1ii2卢pos1
wait,wait wait push,push
pos1
November 6, 2013 15/48
Example: Robots and Carriage wait,wait push,push
it ,wa h us
sh pu
pos0
it,p
pu
pos0 wa
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sh ,w ait wa it,p us h
q0
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Leon van der Torre 路 University of Luxembourg
q1
hh1ii2卢pos1
wait,wait push,push
pos1
November 6, 2013 15/48
Example: Robots and Carriage wait,wait push,push
it ,wa h us
sh pu
pos0
it,p
pu
pos0 wa
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sh ,w ait wa it,p us h
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Leon van der Torre 路 University of Luxembourg
q1
hh1ii2卢pos1
wait,wait push,push
pos1
November 6, 2013 15/48
Agreement technologies
1
Semantics: alignment, interoperability, ontologies
Leon van der Torre 路 University of Luxembourg
November 6, 2013 16/48
Agreement technologies
1
Semantics: alignment, interoperability, ontologies
2
Norms: deontic logic, legal context
Leon van der Torre 路 University of Luxembourg
November 6, 2013 16/48
Agreement technologies
1
Semantics: alignment, interoperability, ontologies
2
Norms: deontic logic, legal context
3
Organisation: roles, social networks, dependence networks
Leon van der Torre 路 University of Luxembourg
November 6, 2013 16/48
Agreement technologies
1
Semantics: alignment, interoperability, ontologies
2
Norms: deontic logic, legal context
3
Organisation: roles, social networks, dependence networks
4
Argumentation: negotiation
Leon van der Torre 路 University of Luxembourg
November 6, 2013 16/48
Agreement technologies
1
Semantics: alignment, interoperability, ontologies
2
Norms: deontic logic, legal context
3
Organisation: roles, social networks, dependence networks
4
Argumentation: negotiation
5
Trust and reputation management
Leon van der Torre 路 University of Luxembourg
November 6, 2013 16/48
Agreement technologies
1
Semantics: alignment, interoperability, ontologies
2
Norms: deontic logic, legal context
3
Organisation: roles, social networks, dependence networks
4
Argumentation: negotiation
5
Trust and reputation management
Besides economic theories, also legal reasoning, linguistics, and sociology
Leon van der Torre 路 University of Luxembourg
November 6, 2013 16/48
Agreement technologies Billhardt et al. (2011) envision that methods and mechanisms from the fields of semantic alignment, norms, organization, argumentation and negotiation, as well as trust and reputation are part of a “sandbox” to build software systems based on a technology of agreement.
Leon van der Torre · University of Luxembourg
November 6, 2013 17/48
Agreement technologies Billhardt et al. (2011) envision that methods and mechanisms from the fields of semantic alignment, norms, organization, argumentation and negotiation, as well as trust and reputation are part of a “sandbox� to build software systems based on a technology of agreement. Based on a well known definition of coordination as management of dependencies between organisational activities, they distinguish the detection of dependencies from taking a decision on which coordination action to apply.
Leon van der Torre ¡ University of Luxembourg
November 6, 2013 17/48
Agreement technologies Billhardt et al. (2011) envision that methods and mechanisms from the fields of semantic alignment, norms, organization, argumentation and negotiation, as well as trust and reputation are part of a “sandbox” to build software systems based on a technology of agreement. Based on a well known definition of coordination as management of dependencies between organisational activities, they distinguish the detection of dependencies from taking a decision on which coordination action to apply. Their call-by-agreement interaction method first establishes an agreement for action, and the actual enactment of the action is requested thereafter.
Leon van der Torre · University of Luxembourg
November 6, 2013 17/48
Agreement technologies Billhardt et al. (2011) envision that methods and mechanisms from the fields of semantic alignment, norms, organization, argumentation and negotiation, as well as trust and reputation are part of a “sandbox” to build software systems based on a technology of agreement. Based on a well known definition of coordination as management of dependencies between organisational activities, they distinguish the detection of dependencies from taking a decision on which coordination action to apply. Their call-by-agreement interaction method first establishes an agreement for action, and the actual enactment of the action is requested thereafter. The normative context determines rules of the game, i.e. interaction patterns and additional restrictions.
Leon van der Torre · University of Luxembourg
November 6, 2013 17/48
Agreement technologies
Leon van der Torre 路 University of Luxembourg
November 6, 2013 18/48
Agreement technologies Semantic technologies form the basis to deal with semantic mismatches and alignment of ontologies to give a common understanding of norms or agreements, defining the set of possible agreements.
Leon van der Torre 路 University of Luxembourg
November 6, 2013 19/48
Agreement technologies Semantic technologies form the basis to deal with semantic mismatches and alignment of ontologies to give a common understanding of norms or agreements, defining the set of possible agreements. Norms and organizations determine constraints that the agreements, and the processes to reach them, have to satisfy.
Leon van der Torre 路 University of Luxembourg
November 6, 2013 19/48
Agreement technologies Semantic technologies form the basis to deal with semantic mismatches and alignment of ontologies to give a common understanding of norms or agreements, defining the set of possible agreements. Norms and organizations determine constraints that the agreements, and the processes to reach them, have to satisfy. Organisational structures define the capabilities of the roles and the power and authority relationships among them.
Leon van der Torre 路 University of Luxembourg
November 6, 2013 19/48
Agreement technologies Semantic technologies form the basis to deal with semantic mismatches and alignment of ontologies to give a common understanding of norms or agreements, defining the set of possible agreements. Norms and organizations determine constraints that the agreements, and the processes to reach them, have to satisfy. Organisational structures define the capabilities of the roles and the power and authority relationships among them. Argumentation and negotiation methods are used to make agents reach agreements.
Leon van der Torre 路 University of Luxembourg
November 6, 2013 19/48
Agreement technologies Semantic technologies form the basis to deal with semantic mismatches and alignment of ontologies to give a common understanding of norms or agreements, defining the set of possible agreements. Norms and organizations determine constraints that the agreements, and the processes to reach them, have to satisfy. Organisational structures define the capabilities of the roles and the power and authority relationships among them. Argumentation and negotiation methods are used to make agents reach agreements. The agents use trust mechanisms that summarise the history of agreements and subsequent agreement executions in order to build long-term relationships between the agents.
Leon van der Torre 路 University of Luxembourg
November 6, 2013 19/48
Agreement technologies Semantic technologies form the basis to deal with semantic mismatches and alignment of ontologies to give a common understanding of norms or agreements, defining the set of possible agreements. Norms and organizations determine constraints that the agreements, and the processes to reach them, have to satisfy. Organisational structures define the capabilities of the roles and the power and authority relationships among them. Argumentation and negotiation methods are used to make agents reach agreements. The agents use trust mechanisms that summarise the history of agreements and subsequent agreement executions in order to build long-term relationships between the agents. Billhardt et al. emphasize that these methods may well benefit from each other. Leon van der Torre 路 University of Luxembourg
November 6, 2013 19/48
Reasoning for agreement technologies Trustworthiness / reputation Trust update Violation detection Commitments / intentions Derivation acceptable agreements Construction argumentation framework Interdependencies Derivation potential agreements Identification of powers of agents Institut. facts
Obligations
Generation deontics Interpretation of norms
Collective judgments
Norms
Desires Goals Values
Judgment aggregation Anchoring and grounding Individual judgments Leon van der Torre 路 University of Luxembourg
November 6, 2013 20/48
ASPIC framework: overview Argument structure: Trees where
Nodes are wff of a logical language L Links are applications of inference rules
Rs = Strict rules (φ1, ..., φn → φ); or Rd= Defeasible rules (φ1, ..., φn ⇒ φ)
Reasoning starts from a knowledge base K ⊆ L
Defeat: attack on conclusion, premise or inference, + preferences Argument acceptability based on Dung (1995)
Leon van der Torre · University of Luxembourg
Slide by Henry Prakken
November 6, 2013 21/48
We should lower taxes
Lower taxes increase productivity
Increased productivity is good
Leon van der Torre 路 University of Luxembourg
Slide by Henry Prakken
November 6, 2013 22/48
We should lower taxes
Lower taxes increase productivity
Increased productivity is good
Leon van der Torre 路 University of Luxembourg
We should not lower taxes
Lower taxes increase inequality
Increased inequality is bad
Slide by Henry Prakken
November 6, 2013 23/48
We should lower taxes
Lower taxes increase productivity
We should not lower taxes
Increased productivity is good
Leon van der Torre 路 University of Luxembourg
Lower taxes increase inequality
Increased inequality is bad
Lower taxes do not increase productivity
USA lowered taxes but productivity decreased
Slide by Henry Prakken
November 6, 2013 24/48
We should lower taxes
Lower taxes increase productivity
We should not lower taxes
Increased productivity is good
Prof. P says that …
Leon van der Torre · University of Luxembourg
Lower taxes increase inequality
Increased inequality is bad
Lower taxes do not increase productivity
USA lowered taxes but productivity decreased
Slide by Henry Prakken
November 6, 2013 25/48
We should lower taxes
Lower taxes increase productivity
Prof. P says that …
People with political ambitions are not objective
We should not lower taxes
Increased productivity is good
Prof. P is not objective
Prof. P has political ambitions
Leon van der Torre · University of Luxembourg
Lower taxes increase inequality
Increased inequality is bad
Lower taxes do not increase productivity
USA lowered taxes but productivity decreased
Slide by Henry Prakken
November 6, 2013 26/48
We should lower taxes
Lower taxes increase productivity
Prof. P says that …
People with political ambitions are not objective
We should not lower taxes
Increased productivity is good
Prof. P is not objective
Prof. P has political ambitions
Leon van der Torre · University of Luxembourg
Lower taxes increase inequality
Increased inequality is bad
Lower taxes do not increase productivity
USA lowered taxes but productivity decreased
Slide by Henry Prakken
November 6, 2013 27/48
We should lower taxes
Lower taxes increase productivity
Prof. P says that ‌
People with political ambitions are not objective
We should not lower taxes
Increased productivity is good
Prof. P is not objective
Prof. P has political ambitions
Leon van der Torre ¡ University of Luxembourg
Lower taxes increase inequality
Increased inequality is good
Lower taxes do not increase productivity
USA lowered taxes but productivity decreased
Increased inequality is bad
Increased inequality stimulates competition
Competition is good
Slide by Henry Prakken
November 6, 2013 28/48
Argumentation systems
An argumentation system is a tuple AS = (L, -,R, ≤) where:
L is a logical language - is a contrariness function from L to 2L R = Rs ∪Rd is a set of strict and defeasible inference rules ≤ is a partial preorder on Rd
S ⊆ L is (directly) consistent iff for no φ, ψ ∈ L it holds that φ ∈ -(ψ)
Leon van der Torre · University of Luxembourg
Slide by Henry Prakken
November 6, 2013 29/48
Knowledge bases
A knowledge base in AS = (L, -,R,≤’) is a pair (K, ≤’) where K ⊆ L and K is a partition Kn ∪ Kp ∪ Ka ∪ Ki where: Kn = necessary premises Kp = ordinary premises Ka = assumptions Ki = issues (ignored below) Moreover, ≤’ is a partial preorder on K/Kn.
Leon van der Torre · University of Luxembourg
Slide by Henry Prakken
November 6, 2013 30/48
Structure of arguments
An argument A on the basis of (K,≤’) in (L, -,R,≤) is:
φ if φ ∈ K with
Prem(A) = {φ}, Conc(A) = φ, Sub(A) = {φ}
A1, ..., An →/⇒ φ if there is a strict/defeasible inference rule Conc(A1), ..., Conc(An) →/⇒ φ
Prem(A) = Prem(A1) ∪ ... ∪ Prem(An) Conc(A) = φ Sub(A) = Sub(A1) ∪ ... ∪ Sub(An) ∪ {A}
Leon van der Torre · University of Luxembourg
Slide by Henry Prakken
November 6, 2013 31/48
Rs:
Rd :
p,q → s u,v → w
p⇒t s,r,t ⇒ v
Kn = {q}
w
u, v → w ∈ Rs
p
v
p, q → s ∈ Rs
Kp = {p,u}
Ka = {r}
A1 = p
A5 = A1 ⇒ t
A2 = q
A6 = A1,A2 → s
A3 = r
A7 = A5,A3,A6 ⇒ v
A4 = u
A8 = A7,A4 → w
u s,r,t ⇒ v ∈ Rd a
r
s p
p
t
n
q
p
p ⇒ t ∈ Rd
p
Leon van der Torre · University of Luxembourg
Slide by Henry Prakken
November 6, 2013 32/48
Argumentation theories
An argumentation theory is a triple AT = (AS,KB,≤a) where:
AS is an argumentation system KB is a knowledge base in AS ≤a is an argument ordering on ArgsAT where
ArgsAT = {A | A is an argument on the basis of KB in AS}
Leon van der Torre · University of Luxembourg
Slide by Henry Prakken
November 6, 2013 33/48
Attack and defeat (with symmetric and Ka = ∅) -
A undermines B (on φ) if Conc(A) = -φ for some φ ∈ Prem(B )/ Kn; A rebuts B (on B’ ) if
A undercuts B (on B’ ) if
Naming convention Conc(A) = -Conc(B’ ) for some B’ ∈ Sub( B ) with a defeasible top implicit rule
Conc(A) = -r ’for some B’ ∈ Sub(B ) with defeasible top rule r
A defeats B iff for some B’ A undermines B on φ and not A <a φ ; or
A rebuts B on B’ and not A <a B’ ; or A undercuts B on B’
Direct vs. subargument attack/defeat Preference-dependent vs. preference-independent attacks
Leon van der Torre · University of Luxembourg
Slide by Henry Prakken
November 6, 2013 34/48
Rs:
Rd :
p,q → s u,v → w
p⇒t s,r,t ⇒ v
Kn = {q}
w
p
v
Kp = {p,u}
Ka = {r}
A1 = p
A5 = A1 ⇒ t
A2 = q
A6 = A1,A2 → s
A3 = r
A7 = A5,A3,A6 ⇒ v
A4 = u
A8 = A7,A4 → w
u a
r
s p
p
t
n
q
p
p
Leon van der Torre · University of Luxembourg
Slide by Henry Prakken
November 6, 2013 35/48
Argument acceptability
Dung-style semantics applied to (ArgsAT , defeatAT)
Leon van der Torre · University of Luxembourg
Slide by Henry Prakken
November 6, 2013 36/48
We should lower taxes
Lower taxes increase productivity
Prof. P says that â&#x20AC;Ś
People with political ambitions are not objective
We should not lower taxes
Increased productivity is good
Prof. P is not objective
Prof. P has political ambitions
Leon van der Torre ¡ University of Luxembourg
Lower taxes increase inequality
Increased inequality is good
Lower taxes do not increase productivity
USA lowered taxes but productivity decreased
Increased inequality is bad
Increased inequality stimulates competition
Competition is good
Slide by Henry Prakken
November 6, 2013 37/48
A
C
Leon van der Torre 路 University of Luxembourg
B
D
E
Slide by Henry Prakken
November 6, 2013 38/48
A
B
A’ C
Leon van der Torre · University of Luxembourg
D
E
Slide by Henry Prakken
November 6, 2013 39/48
P1
P2
P3
A
P4 B
A’
P5
E
D
C P6
Leon van der Torre · University of Luxembourg
P7
P8
P9 Slide by Henry Prakken
November 6, 2013 40/48
Summary logics in MAS Interaction 1 Choosing: the best decision by combining beliefs and preference
Leon van der Torre 路 University of Luxembourg
November 6, 2013 41/48
Summary logics in MAS Interaction 1 Choosing: the best decision by combining beliefs and preference 2 Planning: by creating and revising intentions
Leon van der Torre 路 University of Luxembourg
November 6, 2013 41/48
Summary logics in MAS Interaction 1 Choosing: the best decision by combining beliefs and preference 2 Planning: by creating and revising intentions 3 Strategizing: by the power of coalitions
Leon van der Torre 路 University of Luxembourg
November 6, 2013 41/48
Summary logics in MAS Interaction 1 Choosing: the best decision by combining beliefs and preference 2 Planning: by creating and revising intentions 3 Strategizing: by the power of coalitions 4 Aggregating: preferences and beliefs
Leon van der Torre 路 University of Luxembourg
November 6, 2013 41/48
Summary logics in MAS Interaction 1 Choosing: the best decision by combining beliefs and preference 2 Planning: by creating and revising intentions 3 Strategizing: by the power of coalitions 4 Aggregating: preferences and beliefs 5 Incentivizing: by creating social laws
Leon van der Torre 路 University of Luxembourg
November 6, 2013 41/48
Summary logics in MAS Interaction 1 Choosing: the best decision by combining beliefs and preference 2 Planning: by creating and revising intentions 3 Strategizing: by the power of coalitions 4 Aggregating: preferences and beliefs 5 Incentivizing: by creating social laws Coordination: 1 Grounding: shared beliefs and norms
Leon van der Torre 路 University of Luxembourg
November 6, 2013 41/48
Summary logics in MAS Interaction 1 Choosing: the best decision by combining beliefs and preference 2 Planning: by creating and revising intentions 3 Strategizing: by the power of coalitions 4 Aggregating: preferences and beliefs 5 Incentivizing: by creating social laws Coordination: 1 Grounding: shared beliefs and norms 2 Framing: agreements using norms
Leon van der Torre 路 University of Luxembourg
November 6, 2013 41/48
Summary logics in MAS Interaction 1 Choosing: the best decision by combining beliefs and preference 2 Planning: by creating and revising intentions 3 Strategizing: by the power of coalitions 4 Aggregating: preferences and beliefs 5 Incentivizing: by creating social laws Coordination: 1 Grounding: shared beliefs and norms 2 Framing: agreements using norms 3 Optioning: agreements within organizations
Leon van der Torre 路 University of Luxembourg
November 6, 2013 41/48
Summary logics in MAS Interaction 1 Choosing: the best decision by combining beliefs and preference 2 Planning: by creating and revising intentions 3 Strategizing: by the power of coalitions 4 Aggregating: preferences and beliefs 5 Incentivizing: by creating social laws Coordination: 1 Grounding: shared beliefs and norms 2 Framing: agreements using norms 3 Optioning: agreements within organizations 4 Agreeing: by argumentation and negotiation
Leon van der Torre 路 University of Luxembourg
November 6, 2013 41/48
Summary logics in MAS Interaction 1 Choosing: the best decision by combining beliefs and preference 2 Planning: by creating and revising intentions 3 Strategizing: by the power of coalitions 4 Aggregating: preferences and beliefs 5 Incentivizing: by creating social laws Coordination: 1 Grounding: shared beliefs and norms 2 Framing: agreements using norms 3 Optioning: agreements within organizations 4 Agreeing: by argumentation and negotiation 5 Evaluating: agreements to infer trust
Leon van der Torre 路 University of Luxembourg
November 6, 2013 41/48
What are the challenges for reasoning in law?
Leon van der Torre 路 University of Luxembourg
November 6, 2013 42/48
What are the challenges for reasoning in law?
Combining logics
Leon van der Torre 路 University of Luxembourg
November 6, 2013 42/48
What are the challenges for reasoning in law?
Combining logics (as in other disciplines)
Leon van der Torre 路 University of Luxembourg
November 6, 2013 42/48
What are the challenges for reasoning in law?
Combining logics (as in other disciplines) Norms are more than rules. . .
Leon van der Torre 路 University of Luxembourg
November 6, 2013 42/48
What are the challenges for reasoning in law?
Combining logics (as in other disciplines) Norms are more than rules. . . Linguistic nature of legal reasoning
Leon van der Torre 路 University of Luxembourg
November 6, 2013 42/48
What are the challenges for reasoning in law?
Combining logics (as in other disciplines) Norms are more than rules. . . Linguistic nature of legal reasoning (Condoravdi & van der Torre, ESSLLI2014)
Leon van der Torre 路 University of Luxembourg
November 6, 2013 42/48
Benefits Preference-based modal logic for conditionals and counterfactuals from the sixties and seventies is a common root for both: the deontic logic community, centered around the biannual conference on deontic logic in computer science, and a growing number of researchers in linguistics and philosophy studying deontic modality in language. First, although the two communities have since drifted apart, there is a clear benefit in taking both perspectives. 1 On the one hand, a logical analysis of the linguistic framework as developed by Kratzer, as well as potential modifications and alternatives, can be used to further develop such frameworks. 2 On the other hand, a more general linguistic analysis of paradoxes and use of normative language can be used to further develop the logic of obligations and permissions. Condoravdi & van der Torre, ESSLLI 2014 Leon van der Torre 路 University of Luxembourg
November 6, 2013 43/48
Linguistic interpretation of Chisholm’s set The most notorious story from the deontic logic literature is known as Chisholm’s paradox: 1 a certain man ought to go to the assistance of his neighbours, 2 if he goes, he ought to tell them he is coming, 3 if he does not go, he ought not to tell them he is coming, and 4 he does not go. It is called a paradox because the standard deontic logic formalization is either inconsistent, or one of the sentences follows logically from the others. Analyses of the three conditional obligations have led to preference-based deontic logic, temporal deontic logic, action deontic logic, non-monotonic deontic logic, and more. A more general linguistic analysis would also question the fourth sentence: what does it mean that the man does not go? Does it mean that he cannot go, that he intends not to go, or that he did not go? Condoravdi & van der Torre, ESSLLI 2014 Leon van der Torre · University of Luxembourg
November 6, 2013 44/48
Emerging frameworks
They are much more similar than is popularly believed, and we expect a synthesis in the coming years. Moreover, there is a common interest in going beyond obligation to other modalities, and their role in decision making. Condoravdi & van der Torre, ESSLLI 2014
Leon van der Torre 路 University of Luxembourg
November 6, 2013 45/48
Anankastic conditionals and BDI-O logic Example: if we want to go to Brooklyn, then we should take the A train. W (Brooklyn) ! O(takeAtrain) using W for want and O for obligation, or write [takeAtrain]Brooklyn to express that Brooklyn is a postcondition of the action takeAtrain, or G(Brooklyn) ! I(takeAtrain) to express that the goal to go to Brooklyn leads to the intention to take the A train. A logical analysis of these formalizations would tell us which inferences come through and which are prevented, predicting, for instance, whether we should be robbed in Brooklyn if one is normally robbed there. Moreover, a logical analysis would reveal interactions between dfferent conditions, for instance, what can be concluded if we add G(Brooklyn ^ takeAtrain) ! I(buy ticket in advance). Such logical considerations can thus inform a linguistically motivated semantics for anankastic conditionals. Condoravdi & van der Torre, ESSLLI 2014 Leon van der Torre · University of Luxembourg
November 6, 2013 46/48
Barriers to the inter-disciplinary work
For a linguist, it is difficult to distinguish between logical alternatives and to assess their relevance and adequacy. For a logician, it is hard to systematically map language to logic and to formalize the use of normative language. Condoravdi & van der Torre, ESSLLI 2014
Leon van der Torre · University of Luxembourg
November 6, 2013 47/48
Summary 1
2
3
Why do we need formal models of reasoning in law? I argue we need formal models for law for interdisciplinarity: law is hard to understand for people outside the area, like computer scientists. Which formal models are best for reasoning in law? I argue for logics developed in multiagent systems, distinguishing traditional formalisms of economic models (decision, game, social choice, processes, mechanism design) and agreement technologies (semantics, norms, organisation, argumentation, trust). What are the challenges for reasoning in law? I argue that the main gap between existing formalisms and legal reasoning is the linguistic nature of the latter, and I argue for a further synthesis of linguistic theories and theories discussed under item 2.
Leon van der Torre 路 University of Luxembourg
November 6, 2013 48/48