Cerutti--PhD viva voce defence

University of BresciaDepartment of Information Engineering

Knowledge Engineering and Human-Computer Interaction Research Group

Argumentation-Based Practical Reasoning

New Models and Algorithms

Federico Cerutti

Thursday 29th March, 2012

c© 2012 Federico Cerutti <[email protected]>

Practical Reasoning Support as �Good Advices�[Girle et al., 2003]

The advice should be presented in a form which can be readilyunderstood by decision makers

There should be ready access to both information and reasoningunderpinning the advice

If decision support involves details which are unusual to thedecision maker, it is of primary importance that s/he can discussthese details with his advisor

c© 2012 Federico Cerutti <[email protected]> Thursday 29th March, 2012 2

Practical Reasoning

Knowledge Representation

Computation of Outcomes

Dialogue Models

Computational Argumentation

Rich and interdisciplinary area of research;

for commonsense reasoning;

for con�ict resolution in computer science applications.

[Argumentation is] a verbal and social activity of reasonaimed at increasing (or decreasing) the acceptability of acontroversial standpoint for the listener or reader, by puttingforward a constellation of propositions intended to justify (orrefute) the standpoint before a rational judge.[van Eemeren et al., 1996, p. 5]


History of the Research


An Approach based on Four Components

Argument Schemes

Analysis of existing schemes;New schemes speci�cally designed for practical reasoning;

Critique Schemes

Novel concept giving us a presumption in favour of a critiquebetween argumentation elements;

Evaluation Schemes

Analysis of proposed approaches;Novel formalism extending an existing one:

a framework for encompassing an unrestricted recursive notion ofattack to attack;an approach for describing in�nite argumentation frameworksthrough formal languages;

Dialogue Schemes

Preliminary approach considering HCI issues in the design of adialogue [not covered in this presentation].


Outline of the Presentation

1 Semi-formal Representation:

argument schemes and critique schemes;

2 Formal Representation and Computation:

a new formalism for allowing recursive attacks and thus beinguseful for computing the �nal outcomes of a practical reasoningprocess;

3 In�nite Argumentation Frameworks:

an approach using formal languages for describing in�niteargumentation frameworks and for computing the semanticsextensions on them.


Semi-formal RepresentationFormal Representation and Computation

In�nite Argumentation FrameworksConclusions and Future works


Background: Walton et al. approach[Walton, 1996]

Practical Inference

Major Premise: I have a goal G.

Minor Premise: Carrying out this action A is a means to realise G.

Conclusion: Therefore, I ought to carry out this action A.

CQ1: What other goals that I have that might con�icts with G should be considered?

CQ2: What alternative actions to my bringing about A that would also bring about G

should be considered?

CQ3: Among bringing about A and these alternative actions, which is arguably the most

e�cient?

CQ4: What grounds are there for arguing that it is practically possible for me to bring

about A?

CQ5: What consequences of my bringing about A should also be taken into account?

+ Possibility to chain practical arguments;

- Lack of formalisation;

- Unclear how and when posing a critical question can give rise to a defeat.


Background: Atkinson et al. approach[Atkinson et al., 2004]

AS1 In the current circumstances RWe should perform action AWhich will result in new circumstances SWhich will realise goal GWhich will promote some value V

CQ1 Are the believed circumstances true?

CQ2 Assuming the circumstances, does the action have the stated consequences?

CQ3 Assuming the circumstances and that the action has the statedconsequences, will the action bring about the desired goal?

. . .

+ High level of formalisation;

- Arguments cannot be chained together;

- Unclear when critical questions are posed.


Semi-formal Representation Models: NewConcepts

Six new argument schemes for practical reasoning:

the base set, comprising the practical argument scheme, and theevidence argument scheme;the additional set, considering the value argument scheme, thepreference and auditor argument scheme, and the emotionalargument scheme;improvement of the formalisation level still keeping simpleformalisation and the possibility to chain arguments together;

New concept of critique scheme:

reasoning pattern giving us a presumption in favour of a critiqueamong argumentation elements (arguments or critiques);solve (part of) questions concerning burden of proof;explicit description of what happen with a critique.


Example (1)

John is a non-governmental organisation volunteer who is aboutto go to Brazil for awhile;

John su�ers from disc herniation;

There are three possible actions for treating this disease:

1 take analgesics (and thus be free to go to Brazil);2 have a surgery;3 have a long non-invasive treatment with drugs.


Practical Arguments

JA2: goal: reducing disc herniation,action: have discectomy surgery,state: disc cut,condition: {John su�ers from pain due to spinal dischernia},exception: {anaesthesia allergy and no alternativeanaesthesia}.


Critiques Between Practical Arguments

IJA = {〈take analgesics, have discectomy surgery〉,〈have discectomy surgery, take analgesics〉,〈take analgesics, have long non-invasive treatment〉, . . .}

JPCS1a: source: JA1 instance of PAS,target: JA2 instance of PAS,condition: 〈source.action, target.action〉 ∈ IJA.


Example (2)

John has a history of anaesthesia allergy;

A physician, after some tests, informs John that there is a newkind of anaesthesia to which he is not allergic.


Evidence Arguments and Critiques

JA4: evidence: anaesthesia allergy and no alternative anaesthesia.

JEvCS-exsat1: source: JA4 instance of EvAS,target: JA2 instance of PAS,condition: target.exception ∈Ev-sat-Ex(source.evidence).

JEvCS1: source: JA5 instance of EvAS,target: JA4 instance of EvAS,condition: 〈source.evidence, target.evidence〉 ∈ IJ

Ev.


Example (3)

The action �take analgesics� lets John to be free to go to Brazil,thus promoting the value of charity;

Both the actions �have a discectomy surgery� and �have a longnon-invasive treatment with drugs� promote the value of safety.

A value justi�es a goal (e.g. the value of �safety� justi�es the goalof �reducing disc herniation�), which is similar to goals whichjustify actions (e.g. the goal �reducing disc herniation� justi�esthe action �have discectomy surgery�);

Values and practical arguments are strongly related, and thisgives rise to a defence provided by the values in favour of therelated practical arguments.


Value Arguments

JV1: value: charity,goal: being free to go to Brazil,condition: {},exception: {}.

JV2: value: safety,goal: reducing disc herniation,condition: {},exception: {}.


Critiques Concerning Value Arguments


JVDef1.2: source: JV2 instance of VAS,target: JPCS1a instance of PCS,defended: target.target instance of PAS,condition: target.target ∈ V-chain-P(source) and target.source ∈ V-chain-P(x),x instance of VAS and x 6= JV2.

JVDef2.3: source: JV2 instance of VAS,target: JVDef1.1 instance of VDef1,defended: target.target.source instanceof PAS,condition: target.source 6= source andtarget.target.source ∈V-chain-P(source).

JEvVCS1:source: JA4 instance ofEvAS,target: JVDef1.2 instance ofVDef1 or VDef2,condition:

target.defended.exception ∈Ev-sat-Ex(source.evidence) andsource ∈P-chain-V(target.defended).

Example (4)

Between a long non-invasive treatment and a discectomy surgery,John prefers the surgery because it is quicker;

Moreover, since the evidence informing that there is a new kindof anaesthesia to which John is not allergic results from a clinicaltest, this evidence is preferable over the other informing thatJohn has a history of anaesthesia allergy;

In this situation, John can counterbalance the preferencesbetween the two values, in order to analyse di�erent what-ifsituations.


Preference (and Auditor) Arguments

JPe1: preferred: anaesthesia allergy and no alternative anaesthesia,notpreferred: anaesthesia allergy and alternative anaesthesia,condition: {test result},exception: {}.

JPa1: preferred: having discectomy surgery,notpreferred: having long non-invasive treatment,condition: {surgery is quicker},exception: {}.

JM1: preferred: safety,notpreferred: charity,condition: {},exception: {}.


Critiques Concerning Preference (and Auditor)Arguments


JPraCS1: source: JPa1 instance of PraAS,target: JPCS3b instance of PCS,condition: source.preferred = target.target.action and source.notpreferred =target.source.action.

JMCS1: source: JM1 instance of MAS,target: JVDef2.1 instance of VDef2,condition: source.notpreferred =target.source.value and source.preferred =target.target.source.value.

JPrRebCS1:source: JM1 instance of PraASor PreAS or PrvAS,target: JM2 instance of PraASor PreAS or PrvAS,condition: JM1.preferred =JM2.notpreferred andJM1.notpreferred =JM2.preferred.

Example (5)

Unfortunately, John is frightened by surgeries. . .


Emotional Arguments and Critiques


JE1: emotion: surgery frightened,object: having discectomy surgery,feeling: unfavourable.

JEmCS1: source: JE1 instance of EmAS,target: JA2 instance of PAS,condition: source.object =target.action and source.feeling =unfavourable.

Semi-formal Representation Models: Summary

Six new argument schemes for practical reasoning;

Improvement of the formalisms w.r.t. literature;

New notion of critique scheme;

Burden of proof and results of the critique explicitly considered.


Semi-formal Representation

Formal Representation andComputation

In�nite Argumentation FrameworksConclusions and Future works


Background: Abstract Argumentation Framework[Dung, 1995]

De�nition

An argumentation framework (af) is a pair 〈A,→〉 where A is a set ofarguments and →⊆ A×A is a binary relation of attack or defeat on it.

{A,E} is a D-con�ict-free set;

E is D-acceptable w.r.t. (is defended by) {C};F({C}) = {C,E} (D-characteristic function);{A} is a D-admissible set.


Background: Abstract Argumentation Framework[Dung, 1995]

De�nition

An argumentation framework (af) is a pair 〈A,→〉 where A is a set ofarguments and →⊆ A×A is a binary relation of attack or defeat on it.

D-Grounded extension , the least �xed point of theD-characteristic function: {C,E};D-Preferred extension , a maximal (w.r.t. set inclusion)D-admissible sets: {A,C,E}, {B,C,E}.


Background: Value-based ArgumentationFramework [Bench-Capon and Atkinson, 2009]

De�nition

A value-based argumentation framework (V AF ) is a 5-tupleV AF = 〈AV,→V,V, val,P〉 where 〈AV,→V〉 is a Dung's AF , V is anon-empty set of values, val is a function which maps from elementsof AV to elements of V; and P is the set of possible audiences (i.e.total orders on V).

Given val(A) = v1, val(B) = v2, if for an audience v2 � v1, then. . .


Background: Value-based ArgumentationFramework [Bench-Capon and Atkinson, 2009]

De�nition

A value-based argumentation framework (V AF ) is a 5-tupleV AF = 〈AV,→V,V, val,P〉 where 〈AV,→V〉 is a Dung's AF , V is anon-empty set of values, val is a function which maps from elementsof AV to elements of V; and P is the set of possible audiences (i.e.total orders on V).

Given val(A) = v1, val(B) = v2, if for an audience v2 � v1, then theattack from A against B is not e�ective.


Background: Extended ArgumentationFramework [Modgil and Prakken, 2010]

De�nition

An EAF is a tuple 〈A, C,D〉, where 〈A, C〉 is a Dung's AF , D ⊆ A×C,and if (Z, (X,Y )), (Z ′, (Y,X)) ∈ D then (Z,Z ′), (Z ′, Z) ∈ C.


Formal Representation and Computation: AFRA,a New Formalism

Requirements:

to provide a formal counterpart to argument and critique schemesshown before;

to encompass an unrestricted recursive notion of attack to attack;

to keep de�nitions for semantics extensions as simple as possible;

to encompass Dung's AF as a special case of the proposedformalism;

to ensure compatibility between the semantics notions in theproposed formalism and those in Dung's AF .


Argumentation Framework with RecursiveAttacks (AFRA)

De�nition (AFRA)

An Argumentation Framework with Recursive Attacks (AFRA) is apair 〈A,R〉 where:

A is a set of arguments;

R is a set of attacks, namely pairs (a,X ) s.t. a ∈ A and (X ∈ Ror X ∈ A).

Given an attack α = (a,X ) ∈ R, we say that a is the source of α,denoted as src(α) = a and X is the target of α, denoted astrg(α) = X .


Semantics for AFRA

α directly defeats B (B = trg(α));

α indirectly defeats β (src(β) = trg(α));

α→R B, α→R β;

{γ, β} is a con�ict-free set (no defeats among the elements in theset);

δ is acceptable w.r.t. {ε};F({ε}) = {A,C,D, δ} (characteristic function);{η, γ} is an admissible set.


Semantics for AFRA

De�nition

Let Γ = 〈A,R〉 be an AFRA, S ⊆ A ∪R:the grounded extension of Γ is the least �xed point of FΓ (e.g.{A,D, η, γ});S is a preferred extension of Γ i� it is a maximal (w.r.t. setinclusion) admissible set (e.g. {A,D, η, γ, β,B} and{A, D, η, γ, α});


Recalling the Example. . .


. . . and the Two Preferred Extensions



In�nite ArgumentationFrameworks

Conclusions and Future works


Background: an Example of In�niteArgumentation Frameworks [Dung, 1995]


({}, even(0))

({}, q(0))

({¬even(0)}, even(1))

({¬even(n− 1)}, even(n))

({¬even(0)},¬even(0))

({¬even(1)},¬even(1))

({¬even(n)},¬even(n))

({¬even(0)}, q(0))

({¬q(0)},¬q(0)) ({¬q(0)}, p)

({¬even(0)}, q(1))

({¬even(1)}, q(1))

({¬q(1)},¬q(1)) ({¬q(1)}, p)

({¬p}, r)

({¬r},¬r)

({¬p},¬p)({¬even(n− 1)}, q(n))

({¬even(n)}, q(n))

({¬q(n)},¬q(n)) ({¬q(n)}, p) r ← ¬pp← ¬q(x)q(x)← even(x)q(x)← ¬even(x)even(s(x))← ¬even(x)even(0)←

Moral Dilemmas in Practical Reasoning: anExample

Fred, a system administrator, receives a helpdesk request fromEve who asks for the release of an email accidentally blocked bysecurity �lters;

Fred �nds out that it is a legal email from Eve's lover, and thushe releases the email;

Since Eve is his best friend's wife, he is wondering whether toinform his friend (and thus promoting the value of Friendship) ornot (according to the Law);

This can give rise to an (in�nite) monologue during which Fredcontinuously goes back and forth between the value of friendshipand the value of law. . .


A Formal Representation of Moral Dilemmas inPractical Reasoning

Each value is committed to protect the associated practical argumentin order to make it to prevail over the other practical argument.


In�nite Argumentation Frameworks: Two Linesof Research

1 Providing suitable mechanisms for representing in�nite AFRAsthrough formal languages and for computing semantics extensionson such formalisms;

2 Extend the approach developed in the case of AFRA also fordealing with in�nite Dung's AF s.


Representing an In�nite AFRA

De�nition

Given an afra 〈X ,R〉 where R ⊂ X ∗ is a regular languagerepresented as a dfaM, its Dfa+ is a representation of 〈X ,R〉 as asingle dfaM+ = 〈X , QM+ , q0, FM+ , δ+〉 such that for any w ∈ X ∗ itholds w ∈ L(M+) if and only if w ∈ X ∪R.


Computing the Grounded Extension of an In�niteAFRA1: Input: Dfa+ M+ = 〈X , QM+ , q0, FM+ , δ+〉 with α ∈ L(M+)⇔ α ∈ X ∪R.2: Output: dfaMG = 〈X , QG, q0, FG, δG〉 with α ∈ L(MG)⇔ α ∈ GE(〈X̃ , R̃〉)3: i := 04: Mi := csplit(M+); withMi = 〈X , Qi, q0, Fi, δi〉5: repeat6: i := i+ 1;Mi := Mi−1;7: For each (unmarked) unattacked state q ofMi mark q as in(i).8: for each unattacked state q and every q′ ∈ state− in(q) ∩ Fi do

9: Mark q′ as out and remove q′ from Fi.10: end for

11: for each x ∈ X s.t. argst(x) is marked out do

12: For each state q ∈ Fi with x ∈ sym− in(q) mark q as out and remove qfrom Fi.

13: end for

14: untilMi =Mi−1

15: for any q ∈ Fi which is not marked in() do16: remove q from Fi

17: end for

18: return 〈X , Qi, q0, Fi, δi〉


Computing the Grounded Extension of an In�niteAFRA

Theorem

LetM+ = 〈X , QM+ , q0, FM+ , δ+〉 with α ∈ L(M+)⇔ α ∈ X ∪R be aDfa

+ describing the afra, 〈X ,R〉 with corresponding af 〈X̃ , R̃〉. Itis possible to construct in polynomial time a dfaMG = 〈X , QG, q0, FG, δG〉 with α ∈ L(MG)⇔ α ∈ GE(〈X̃ , R̃〉).


Describing In�nite Dung's Framework

Argument Encoding: a regular language over an alphabet;

Attack Expression: a sentence considering the symbols of thealphabet, an identity symbol, concatenation symbol, . . .

If we can represent the set of arguments through some �niteautomaton (i.e. a regular language), and we can write an attackexpression that for each word (argument) returns the set of attackers,then there are e�ective algorithms:

1 for deciding if a set of arguments is D-con�ict-free, D-admissible,a D-stable, or a D-complete extension;

2 for computing whether an argument is D-acceptable w.r.t. a set,and the result of the application of the characteristic function ona set of arguments;

3 for determining (in some cases) the D-grounded extension.


In�nite Argumentation Frameworks: Summary

Formal languages provide suitable mechanisms for describingin�nite argumentation frameworks (both AFRA and AF );

Using formal languages there are e�ective algorithms forcomputing several semantics concepts (e.g. we provided apolynomial algorithm for computing the grounded extension of anAFRA even if it has an in�nite set of attacks . . . ).



In�nite Argumentation Frameworks

Conclusions and Futureworks


Conclusions

The Argumentation System for Practical Reasoning comprisingargument, critique, evaluation, and dialogue schemes;

Six new argument schemes speci�cally designed for practical reasoning;

The new concept of critique scheme as a presumption in favour of acritique between argumentation elements;

The Argumentation Framework with Recursive Attacks, a newformalism:

for formal representing instances of practical reasoning argumentand critique schemes and for computing the decision outcomes;for encompassing an unrestricted recursive notion of attack toattack;with bijective correspondence with Dung's AF semantics notions;

Innovative proposal for computing with in�nite frameworks, both in thecase of AFRA and of AF ;

Preliminary proposal of dialogue schemes considering HCI issues.


Future works

Development of the fourth component: complete proposal ofdialogue schemes encompassing our argumentation-basedapproach for practical reasoning;

Implementation of the whole system:

Adoption in real practical reasoning contexts and proving thevalidity of the approach;May suggest further theoretical development;

Theoretical developments in computing with in�nite structures(in particular completing the study of standard decision andconstruction problems).


Argumentation-Based Practical ReasoningNew Models and Algorithms

Federico Cerutti


References I

[Atkinson et al., 2004] Atkinson, K., Capon, T. B., and Mcburney, P. (2004).Justifying practical reasoning.In Reed and Carenini, G., editors, Proceedings of the Fourth Workshop on Computational Modelsof Natural Argument (CMNA 2004), pages 87�90.

[Bench-Capon and Atkinson, 2009] Bench-Capon, T. and Atkinson, K. (2009).Abstract argumentation and values.In Simari, G. and Rahwan, I., editors, Argumentation in Arti�cial Intelligence, pages 45�64.Springer US.

[Dung, 1995] Dung, P. M. (1995).On the acceptability of arguments and its fundamental role in nonmonotonic reasoning, logicprogramming, and n-person games.Arti�cial Intelligence, 77(2):321�357.

[Girle et al., 2003] Girle, R., Hitchcock, D. L., McBurney, P., and Verheij, B. (2003).Decision support for practical reasoning: A theoretical and computational perspective.In Reed, C. and Norman, T. J., editors, Argumentation Machines. New Frontiers in Argumentand Computation, pages 55�84.

[Modgil and Prakken, 2010] Modgil, S. and Prakken, H. (2010).Preferences in structure extended argumentation frameworks.volume 216 of Frontiers in Arti�cial Intelligence. IOS Press.


References II

[van Eemeren et al., 1996] van Eemeren, F. H., Grootendorst, R., Johnson, R. H., Plantin, C., Walton,D. N., Willard, C. A., Woods, J., and Zarefsky, D. (1996).Fundamentals of Argumentation Theory. A Handbook of Historical Backgrounds andContemporary Developments.Lawrence Erlbaum Associates.

[Walton, 1996] Walton, D. N. (1996).Argumentation Schemes for Presumptive Reasoning.Lawrence Erlbaum Associates.


Cerutti--PhD viva voce defence

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