Download presentation

Presentation is loading. Please wait.

Published byNikolas Broadstreet Modified over 2 years ago

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

2
2 Contents Structured argumentation: Arguments Argument schemes

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

4
4 The structure of arguments: two approaches Both approaches: arguments are inference trees Assumption-based approaches (Dung-Kowalski-Toni, Besnard & Hunter, …) Sound reasoning from uncertain premises Arguments attack each other on their assumptions (premises) Rule-based approaches (Pollock, Vreeswijk, …) Risky (‘defeasible’) reasoning from certain premises Arguments attack each other on applications of defeasible inference rules

5
5 Aspic framework: overview Argument structure: Trees where Nodes are wff of a logical language L Links are applications of inference rules R s = Strict rules ( 1,..., 1 ); or R d = Defeasible rules ( 1,..., 1 ) Reasoning starts from a knowledge base K L Defeat: attack on conclusion, premise or inference, + preferences Argument acceptability based on Dung (1995)

6
6 Argumentation systems An argumentation system is a tuple AS = ( L, -, R, ) where: L is a logical language - is a contrariness function from L to 2 L R = R s R d is a set of strict and defeasible inference rules is a partial preorder on R d If - ( ) then: if - ( ) then is a contrary of ; if - ( ) then and are contradictories = _ , = _

7
7 Knowledge bases A knowledge base in AS = ( L, -, R, = ’) is a pair ( K, =< ’) where K L and ’ is a partial preorder on K / K n. Here: K n = (necessary) axioms K p = ordinary premises K a = assumptions

8
8 Structure of arguments An argument A on the basis of ( K, ’) in ( L, -, R, ) is: if K with Conc(A) = { } Sub(A) = DefRules(A) = A 1,..., A n if there is a strict inference rule Conc(A 1 ),..., Conc(A n ) Conc(A) = { } Sub(A) = Sub(A 1 ) ... Sub(A n ) {A} DefRules(A) = DefRules(A 1 ) ... DefRules(A n ) A 1,..., A n if there is a defeasible inference rule Conc(A 1 ),..., Conc(A n ) Conc(A) = { } Sub(A) = Sub(A 1 ) ... Sub(A n ) {A} DefRules(A) = DefRules(A 1 ) ... DefRules(A n ) {A 1,..., A n }

9
9 Q1Q2 P R1R2 R1, R2 Q2 Q1, Q2 P Q1,R1,R2 K

10
10 Example R : r1: p q r2: p,q r r3: s t r4: t ¬r1 r5: u v r6: v,q ¬t r7: p,v ¬s r8: s ¬p K n = { p}, K p = { s,u}

11
11 Types of arguments An argument A is: Strict if DefRules(A) = Defeasible if not Firm if Prem(A) K n Plausible if not firm S |- means there is a strict argument A s.t. Conc(A) = Prem(A) S

12
12 Domain-specific vs. inference general inference rules R1: Bird Flies R2: Penguin Bird Penguin K R d = { , } R s = all deductively valid inference rules Bird Flies K Penguin Bird K Penguin K Flies Bird Penguin Flies Bird Bird Flies Penguin Penguin Bird

13
13 Argument(ation) schemes: general form Defeasible inference rules! But also critical questions Negative answers are counterarguments Premise 1, …, Premise n Therefore (presumably), conclusion

14
14 Expert testimony (Walton 1996) Critical questions: Is E biased? Is P consistent with what other experts say? Is P consistent with known evidence? E is expert on D E says that P P is within D Therefore (presumably), P is the case

15
15 Witness testimony Critical questions: Is W sincere? Does W’s memory function properly? Did W’s senses function properly? W says P W was in the position to observe P Therefore (presumably), P

16
16 Arguments from consequences Critical questions: Does A also have bad consequences? Are there other ways to bring about G?... Action A brings about G, G is good Therefore (presumably), A should be done

17
17 Temporal persistence (Forward) Critical questions: Was P known to be false between T1 and T2? Is the gap between T1 and T2 too long? P is true at T1 and T2 > T1 Therefore (presumably), P is still true at T2

18
18 Temporal persistence (Backward) Critical questions: Was P known to be false between T1 and T2? Is the gap between T1 and T2 too long? P is true at T1 and T2 < T1 Therefore (presumably), P was already true at T2

19
19 X murdered Y Y murdered in house at 4:45 X in 4:45 X in 4:45 {X in 4:30} X in 4:45 {X in 5:00} X left 5:00 W3: “X left 5:00”W1: “X in 4:30” W2: “X in 4:30” X in 4:30 {W1} X in 4:30 {W2} X in 4:30 accrual testimony forw temp pers backw temp pers dmp accrual V murdered in L at T & S was in L at T S murdered V

Similar presentations

Presentation is loading. Please wait....

OK

Inferences The Reasoning Power of Expert Systems.

Inferences The Reasoning Power of Expert Systems.

© 2017 SlidePlayer.com Inc.

All rights reserved.

Ads by Google

Ppt on limits and derivatives tutorial Free ppt on american war of independence Ppt on review writing tips Ppt on water scarcity in the world Weekends by appt only Ppt on spiritual leadership conference Ppt on nouns for class 5 Ppt on media research tools Ppt on types of forests in india Ppt on telling time in spanish