[PPT] - Chapter 16: Rationality Postulates and Critical Examples Martin PowerPoint Presentation

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Chapter 16: Rationality Postulates and Critical Examples

Martin Caminada Department of Computing Science University of Aberdeen

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Outline

(1) introduction

(2) preliminaries (3) direct consistency, indirect consistency and closure a) restricted rebut solutions b) unrestricted rebut solutions (4) non-interference and crash resistance a) erasing inconsistent arguments b) requiring consistent entailment and forbidding strict-on-strict (5) rationality postulates and other instantiations (6) summary and discussion

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Outline

(1) introduction

(2) preliminaries (3) direct consistency, indirect consistency and closure a) restricted rebut solutions b) unrestricted rebut solutions (4) non-interference and crash resistance a) erasing inconsistent arguments b) requiring consistent entailment and forbidding strict-on-strict (5) rationality postulates and other instantiations (6) summary and discussion

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Introduction

explain difference between strict

and defeasible inference steps

problems start when combining these;

this is often required (explain)

in argumentation context, part of the problem

is applying blind semantics (explain)

satisfying a reasonable outcome is far from trivial;

in current chapter we try to specify what a reasonable

utcome is, and how to bring this about

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Outline

(1) introduction

(2) preliminaries (3) direct consistency, indirect consistency and closure a) restricted rebut solutions b) unrestricted rebut solutions (4) non-interference and crash resistance a) erasing inconsistent arguments b) requiring consistent entailment and forbidding strict-on-strict (5) rationality postulates and other instantiations (6) summary and discussion

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Preliminaries

show how to construct arguments

using strict and defeasible rules (simplified ASPIC)

introduce some ways
f dealing with preferences:

elitist vs democratic

distinguish restricted rebut

from unrestricted rebut

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Outline

(1) introduction

(2) preliminaries (3) direct consistency, indirect consistency and closure a) restricted rebut solutions b) unrestricted rebut solutions (4) non-interference and crash resistance a) erasing inconsistent arguments b) requiring consistent entailment and forbidding strict-on-strict (5) rationality postulates and other instantiations (6) summary and discussion

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Direct Consistency, Indirect Consistency and Closure

give Married John example

from (Caminada & Amgoud 2007)

informally explain that under unrestricted rebut,

the example violates closure and indirect consistency

informally explain that under restricted rebut,

the example violates direct consistency

now provide formal definitions of postulates

direct consistency, indirect consistency and closure

mention that two classes of solutions have been found:
ne based on restricted rebut,
ne based on unrestricted rebut

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Outline

(1) introduction

(2) preliminaries (3) direct consistency, indirect consistency and closure a) restricted rebut solutions b) unrestricted rebut solutions (4) non-interference and crash resistance a) erasing inconsistent arguments b) requiring consistent entailment and forbidding strict-on-strict (5) rationality postulates and other instantiations (6) summary and discussion

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Restricted Rebut Solutions

i. transposition
ii. contraposition
iii. semi-abstract approach of Dung&Tang
iv. on the need of complete-based semantics

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Restricted Rebut Solutions

i. transposition
show that Married John example will be OK
provide formal definition of transposition
why do we need restr. rebut? Show tandem example.

problem AA: attack is binary but conflict can be ternary

Theorem:

restr rebut + complete-based sem + transposition = postulates satisfied

ii. contraposition
iii. semi-abstract approach of Dung&Tang
iv. on the need of complete-based semantics

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Restricted Rebut Solutions

i. transposition
ii. contraposition
contraposition is an alternative to transposition
provide formal definition of contraposition

in the context of strict rules

Theorem:

restr rebut + complete-based sem + contraposition = postulates satisfied

iii. semi-abstract approach of Dung&Tang
iv. on the need of complete-based semantics

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Restricted Rebut Solutions

i. transposition
ii. contraposition
iii. semi-abstract approach of Dung&Tang
D&T provide semi-abstract approach

based on subargument structure and attack relation

provide formal definitions
D&T claim their solution is very general:

transposition and contraposition are special cases

however, only works for restricted rebut (!)
iv. on the need of complete-based semantics

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Restricted Rebut Solutions

i. transposition
ii. contraposition
iii. semi-abstract approach of Dung&Tang
iv. on the need of complete-based semantics
the above 3 approaches rely on complete-based sem
things start to fail when applying non-adm-based sem
provide counter example against naive semantics
provide counter example against stage semantics
provide counter example against CF2 semantics
it is not clear how non-adm-based semantics

can be used for any meaningful instantiations

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Outline

(1) introduction

(2) preliminaries (3) direct consistency, indirect consistency and closure a) restricted rebut solutions b) unrestricted rebut solutions (4) non-interference and crash resistance a) erasing inconsistent arguments b) requiring consistent entailment and forbidding strict-on-strict (5) rationality postulates and other instantiations (6) summary and discussion

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Unrestricted Rebut Solutions

provide example COMMA 2014 to illustrate

shortcomings of unrestricted rebut

shortcomings are specially bad in dialogue context
for unrestricted rebut, complete-based semantics is not

sufficient (tandem example) grounded is really needed

Theorem:

unrestricted rebut + grounded sem + transposition = postulates satisfied

works:
when preferences are empty (C&A 2007)
when preferences are total pre-order (CMO 2014)
restricted rebut vs unrestricted rebut:

“every advantage has its disadvantage”

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Outline

(1) introduction

(2) preliminaries (3) direct consistency, indirect consistency and closure a) restricted rebut solutions b) unrestricted rebut solutions (4) non-interference and crash resistance a) erasing inconsistent arguments b) requiring consistent entailment and forbidding strict-on-strict (5) rationality postulates and other instantiations (6) summary and discussion

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Non-Interference and Crash-Resistance

why not use classical logic to generate the strict rules?

transposition would come for free, so easy way of satisfying postulates!

unfortunately: new problem caused by ex falso quodlibet
provide coffee example (BNAIC 2005)
Pollock, Reiter and ASPIC+ tried to solve this

by applying preferred or stable semantics

this still doesn't solve things;

provide unrel John & unrel Mary example (BNAIC 2005)

formally define the additional rationality postulates of

non-interference and crash-resistance

explain that semantics alone cannot solve the problem;

something needs to change on how to construct the graph

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Outline

(1) introduction

(2) preliminaries (3) direct consistency, indirect consistency and closure a) restricted rebut solutions b) unrestricted rebut solutions (4) non-interference and crash resistance a) erasing inconsistent arguments b) requiring consistent entailment and forbidding strict-on-strict (5) rationality postulates and other instantiations (6) summary and discussion

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Erasing Inconsistent Arguments

why not just remove inconsistent arguments,

as these are clearly absurd

warning: removing “absurd” arguments can lead to

problems; self-undercutting arguments cannot be removed (see Pollock's pink elephant example)

we need to show that removing inconsistent arguments

doesn't lead to similar problems; this is far from trivial!

Wu&Podlaszewski proved that removing inconsistent

arguments satisfies all rationality postulates! (Theorem)

their solution only works with restricted rebut,

and when preferences are empty (counterexample Leon)

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Outline

(1) introduction

(2) preliminaries (3) direct consistency, indirect consistency and closure a) restricted rebut solutions b) unrestricted rebut solutions (4) non-interference and crash resistance a) erasing inconsistent arguments b) requiring consistent entailment and forbidding strict-on-strict (5) rationality postulates and other instantiations (6) summary and discussion

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Requiring Consistent Entailment and Forbidding Strict-on-Strict

idea of Grooters & Prakken COMMA 2014
change the way in which strict rules

are generated by classical logic (consistent entailment only)

no strict rule can feed into another strict rule

(have to have defeasible rule in between)

is not just an instantiation of ASPIC+

instead it defines a whole different ASPIC version!

Theorem: all postulates satisfied (are they?)
advantage: it works with preferences (unlike W&P)
disadvantage: works only with restricted rebut

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Outline

(1) introduction

(2) preliminaries (3) direct consistency, indirect consistency and closure a) restricted rebut solutions b) unrestricted rebut solutions (4) non-interference and crash resistance a) erasing inconsistent arguments b) requiring consistent entailment and forbidding strict-on-strict (5) rationality postulates and other instantiations (6) summary and discussion

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Rationality Postulates and Other Instantiations

so far, we have only studied rule-based instantiations
however, similar problems also occur

in classical logic-based instantiations

restricted rebut and unrestricted rebut

have equivalents in logic-based instantiations (Gorogiannis & Hunter 2011)

explain how tandem example works

in Toni Hunter's approach; same problems and space of solution

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Outline

(1) introduction

(2) preliminaries (3) direct consistency, indirect consistency and closure a) restricted rebut solutions b) unrestricted rebut solutions (4) non-interference and crash resistance a) erasing inconsistent arguments b) requiring consistent entailment and forbidding strict-on-strict (5) rationality postulates and other instantiations (6) summary and discussion

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Summary and Discussion

(optionally) provide a table with some of the key results
most papers are on abstract level

most problems are on instantiated level

provide “care home analogy”

to illustrate problem of “blind argument selection”

explain that postulates are not just for logical elegance;

we need these to take into account real world constraints

non-admissibility based semantics are nice on

the abstract level; not so nice on the non-abstract level

if the problem is constraint satisfaction, why not use CAFs?

CAFs don't work on any of the examples! abstract “solutions” make things worse instead of better!

what is it that abstract theories are abstractions of?

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