argumentation logics lecture 5: argumentation with structured arguments (1) argument structure henry...
Post on 14-Dec-2015
225 Views
Preview:
TRANSCRIPT
1
Argumentation LogicsLecture 5:
Argumentation with structured arguments (1)
argument structure
Henry PrakkenChongqing
June 2, 2010
2
Contents Structured argumentation:
Arguments Argument schemes
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
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
Aspic framework: overviewArgument structure: Trees where
Nodes are wff of a logical language L Links are applications of inference rules
Rs = Strict rules (1, ..., 1 ); or Rd= 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
Argumentation systems An argumentation system is a tuple AS = (L,
-,R,) where: L is a logical language - is a contrariness function from L to 2L R = Rs Rd is a set of strict and defeasible inference
rules is a partial preorder on Rd
If -() then: if -() then is a contrary of ; if -() then and are contradictories
= _, = _
7
Knowledge bases A knowledge base in AS = (L, -,R,= ’) is
a pair (K, =<’) where K L and ’ is a partial preorder on K/Kn. Here: Kn = (necessary) axioms Kp = ordinary premises Ka = assumptions
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) =
A1, ..., An if there is a strict inference rule Conc(A1), ..., Conc(An)
Conc(A) = {} Sub(A) = Sub(A1) ... Sub(An) {A} DefRules(A) = DefRules(A1) ... DefRules(An)
A1, ..., An if there is a defeasible inference rule Conc(A1), ..., Conc(An)
Conc(A) = {} Sub(A) = Sub(A1) ... Sub(An) {A} DefRules(A) = DefRules(A1) ... DefRules(An) {A1, ..., An
}
9
Q1 Q2
P
R1 R2
R1, R2 Q2
Q1, Q2 P
Q1,R1,R2 K
10
ExampleR: 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 ¬pKn = {p}, Kp = {s,u}
11
Types of arguments An argument A is:
Strict if DefRules(A) = Defeasible if not Firm if Prem(A) Kn Plausible if not firm
S |- means there is a strict argument A s.t.
Conc(A) = Prem(A) S
12
Domain-specific vs. inference general inference rules
R1: Bird Flies R2: Penguin Bird Penguin K
Rd = {, } Rs = all deductively valid inference rules Bird Flies K Penguin Bird K Penguin K
Flies
Bird
Penguin
Flies
Bird Bird Flies
Penguin Penguin Bird
13
Argument(ation) schemes: general form
Defeasible inference rules! But also critical questions
Negative answers are counterarguments
Premise 1, … , Premise nTherefore (presumably), conclusion
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 DE says that PP is within D Therefore (presumably), P is the case
15
Witness testimony
Critical questions: Is W sincere? Does W’s memory function properly? Did W’s senses function properly?
W says PW was in the position to observe PTherefore (presumably), P
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 goodTherefore (presumably), A should be done
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 > T1Therefore (presumably), P isstill true at T2
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 < T1Therefore (presumably), P was already true at T2
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 testimony
testimony
forwtemp pers
backwtemp pers
dmp
accrual
V murdered in L at T & S was in L at T
S murdered V
top related