Chapter 16: Rationality Postulates and Critical Examples Martin Caminada Department of Computing Science University of Aberdeen
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
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
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 outcome is, and how to bring this about
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
Preliminaries ● show how to construct arguments using strict and defeasible rules (simplified ASPIC) ● introduce some ways of dealing with preferences: elitist vs democratic ● distinguish restricted rebut from unrestricted rebut
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
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: one based on restricted rebut, one based on unrestricted rebut
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
Restricted Rebut Solutions i. transposition ii. contraposition iii. semi-abstract approach of Dung&Tang iv. on the need of complete-based semantics
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
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
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
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
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
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”
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
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
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
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)
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
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
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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