Argumentation Logics Lecture 5 Argumentation with structured arguments

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Argumentation Logics Lecture 5: Argumentation with structured arguments (1) argument structure Henry Prakken Chongqing

Argumentation Logics Lecture 5: Argumentation with structured arguments (1) argument structure Henry Prakken Chongqing June 2, 2010 1

Contents n Structured argumentation: n n n Arguments Argument schemes (Attack and defeat) 2

Contents n Structured argumentation: n n n Arguments Argument schemes (Attack and defeat) 2

Merits of Dung (1995) n Framework for nonmonotonic logics n n Comparison and properties

Merits of Dung (1995) n Framework for nonmonotonic logics n n Comparison and properties Guidance for development From intuitions to theoretical notions But should not be used for practical applications 3

A C B D E 4

A C B D E 4

We should lower taxes Lower taxes increase productivity Prof. P says that … People

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 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 5

Steps in argumentation n n Construct arguments (from a knowledge base) Determine which arguments

Steps in argumentation n n Construct arguments (from a knowledge base) Determine which arguments attack each other Determine which attacking arguments defeat each other (with preferences) Determine the dialectical status of all arguments (justified, defensible or overruled) 6

ASPIC Framework for rulebased argumentation n n Inspired by John Pollock (1987 - 1995)

ASPIC Framework for rulebased argumentation n n Inspired by John Pollock (1987 - 1995) Developed by n n Gerard Vreeswijk (1993, 1997) Leila Amgoud, Martin Caminada, Henry Prakken, . . . (2004 - 2009) 7

Aspic framework: overview Argument structure: n Trees where n n Nodes are wff of

Aspic framework: overview Argument structure: n Trees where n n Nodes are wff of a logical language L Links are applications of inference rules n n n Rs = Strict rules ( 1, . . . , 1 ); or Rd= Defeasible rules ( 1, . . . , 1 ) Reasoning starts from a knowledge base K L Attack: on conclusion, premise or inference Defeat: attack + preferences Dialectical status based on Dung (1995) 8

Argumentation systems n An argumentation system is a tuple AS = (L, -, R,

Argumentation systems n An argumentation system is a tuple AS = (L, -, R, ) where: n n n L is a logical language - is a contrariness function from L to 2 L R = Rs Rd is a set of strict and defeasible inference rules is a partial preorder on Rd If -( ) then: n if ( ) then is a contrary of ; n if ( ) then and are contradictories n n = _ , = _ Example: classical negation as a contrariness function: -( ) = { } if does not start with a negation -( ) = { , } n n 9

Knowledge bases n A knowledge base in AS = (L, -, R, = ’)

Knowledge bases n A knowledge base in AS = (L, -, R, = ’) is a pair (K, ’) where K L and ’ is a partial preorder on K/Kn. Here: n n n Kn = (necessary) axioms Kp = ordinary premises Ka = assumptions 10

Structure of arguments n An argument A on the basis of (K, ’) in

Structure of arguments n An argument A on the basis of (K, ’) in (L, -, R, ) is: n if K with n n A 1, . . . , An if there is a strict inference rule Conc(A 1), . . . , Conc(An) n n Conc(A) = Sub(A) = { } Def. Rules(A) = Conc(A) = Sub(A) = Sub(A 1) . . . Sub(An) {A} Def. Rules(A) = Def. Rules(A 1) . . . Def. Rules(An) A 1, . . . , An if there is a defeasible inference rule Conc(A 1), . . . , Conc(An) n n n Conc(A) = Sub(A) = Sub(A 1) . . . Sub(An) {A} Def. Rules(A) = Def. Rules(A 1) . . . Def. Rules(An) {A 1, . . . , An } 11

P Q 1, R 2 K Q 1, Q 2 P Q 2 R

P Q 1, R 2 K Q 1, Q 2 P Q 2 R 1, R 2 Q 2 R 2 12

Rs = all valid inference rules of propositional and first-order logic Rd = {

Rs = all valid inference rules of propositional and first-order logic Rd = { , } Kp = { (1) Information I concerns health of person P (2) Person P does not agree with publication of information I (3) i is innformation concerning health of person p i is information concerning private life of person p (4) (i is information concerning private of person p & Person p does not agree with publication of information i) It is forbidden to publish information i } -elimination Forbidden to publish I , Rd Implicit! I concerns private life of P & P does not agree with publication of I (i concerns health of p & p does not agree with publication of p ) Forbidden to publish i 1, 2, 3, 4 K I concerns private life of P P does not agree with publication of I , & Rs i concerns health of p i concerns private life of p , Rs I concerns health of P 13

Example R: n r 1: n r 2: n r 3: n r 4:

Example R: n r 1: n r 2: n r 3: n r 4: n r 5: n r 6: n r 7: n r 8: p q p, q r s t t ¬r 1 u v v, q ¬t p, v ¬s s ¬p Kn = {p}, Kp = {s, u} 14

Types of arguments n An argument A is: n n n Strict if Def.

Types of arguments n An argument A is: n n n Strict if Def. Rules(A) = Defeasible if not strict Firm if Prem(A) Kn Plausible if not firm S |- means there is a strict argument A s. t. n n Conc(A) = Prem(A) S 15

Domain-specific vs. inference general inference rules Flies n n n R 1: Bird Flies

Domain-specific vs. inference general inference rules Flies n n n R 1: Bird Flies R 2: Penguin Bird Penguin K Bird Penguin n n Rd = { , } Rs = all deductively valid inference rules Bird Flies K Penguin Bird K Penguin Flies Bird Flies Penguin Bird 16

Argument(ation) schemes: general form Premise 1, …, Premise n Therefore (presumably), conclusion n n

Argument(ation) schemes: general form Premise 1, …, Premise n Therefore (presumably), conclusion n n Defeasible inference rules! But also critical questions n Negative answers are counterarguments 17

Expert testimony (Walton 1996) E is expert on D E says that P P

Expert testimony (Walton 1996) E is expert on D E says that P P is within D Therefore (presumably), P is the case n Critical questions: n n n Is E biased? Is P consistent with what other experts say? Is P consistent with known evidence? 18

Witness testimony W says P W was in the position to observe P Therefore

Witness testimony W says P W was in the position to observe P Therefore (presumably), P n Critical questions: n n n Is W sincere? Does W’s memory function properly? Did W’s senses function properly? 19

Arguments from consequences Action A brings about G, G is good Therefore (presumably), A

Arguments from consequences Action A brings about G, G is good Therefore (presumably), A should be done n Critical questions: n n n Does A also have bad consequences? Are there other ways to bring about G? . . . 20

Temporal persistence (Forward) P is true at T 1 and T 2 > T

Temporal persistence (Forward) P is true at T 1 and T 2 > T 1 Therefore (presumably), P is still true at T 2 n Critical questions: n n Was P known to be false between T 1 and T 2? Is the gap between T 1 and T 2 too long? 21

Temporal persistence (Backward) P is true at T 1 and T 2 < T

Temporal persistence (Backward) P is true at T 1 and T 2 < T 1 Therefore (presumably), P was already true at T 2 n Critical questions: n n Was P known to be false between T 1 and T 2? Is the gap between T 1 and T 2 too long? 22

X murdered Y dmp Y murdered in house at 4: 45 V murdered in

X murdered Y dmp Y murdered in house at 4: 45 V murdered in L at T & S was in L at T S murdered V X in 4: 45{X in 4: 30} forw temp pers testimony W 1: “X in 4: 30” accrual X in 4: 45{X in 5: 00} backw temp pers X in 4: 30{W 1} X in 4: 45 X left 5: 00 X in 4: 30{W 2} testimony W 2: “X in 4: 30” W 3: “X left 5: 00” 23