Default Reasoning

1
Default Reasoning

• Q How many wheels does Johns car have?
• A Four (by default)
• The conclusion is withdrawn if one is supplied
  with the information that one wheel of Johns car
  has just been stolen.

non-monotonicity
2
Default Reasoning

• Q Can bird Tweety fly?
• A Yes (by default)
• The conclusion is withdrawn if it is added that
  Tweety is a penguin.

non-monotonicity
3
Default Reasoning

• Q How many wheels does Johns car have?
• A Four (by default)
• The conclusion is withdrawn if one is supplied
  with the information that one wheel of Johns car
  has just been stolen.
• car(x) ? ? wheel-num(x, 4)

4
Default Reasoning

• Q Can bird Tweety fly?
• A Yes (by default)
• The conclusion is withdrawn if it is added that
  Tweety is a penguin.
• bird(x) ? ? fly(x)

5
Default Reasoning

• Q How many wheels does Johns car have?
• A Four (by default - CWA)
• The conclusion is withdrawn if one is supplied
  with the information that one wheel of Johns car
  has just been stolen.
• car(x) ? ?abnormal(x) ? wheel-num(x, 4)
• wheel-stolen(x) ? abnormal(x)

6
Default Reasoning

• Q Can bird Tweety fly?
• A Yes (by default - CWA)
• The conclusion is withdrawn if it is added that
  Tweety is a penguin.
• bird(x) ? ?abnormal(x) ? fly(x)
• penguin(x) ? abnormal(x)

7
Default Reasoning

• Usually, Quakers are pacifist
• Usually, Republicans are not pacifist
• Richard Nixon is both a Quaker and a Republican
• Q Is Nixon a pacifist?

8
Default Reasoning

• Usually, Quakers are pacifist
• Usually, Republicans are not pacifist
• Richard Nixon is both a Quaker and a Republican

pacifist
Nixon diamond
Quaker
Republican
Nixon
9
Default Reasoning

• Usually, Quakers are pacifist
• Usually, Republicans are not pacifist
• Richard Nixon is both a Quaker and a Republican
• quaker(x) ? ?abnormal1(x) ? pacifist(x)
• republican(x) ? ?abnormal2(x) ? ?pacifist(x)
• quaker(Nixon)
• republican(Nixon)

10
Default Reasoning

• Default consequence
• KB ??D a
• iff a is true in every preferred model of KB.

11
Default Reasoning

• quaker(x) ? ?abnormal1(x) ? pacifist(x)
• republican(x) ? ?abnormal2(x) ? ?pacifist(x)
• quaker(Nixon)
• republican(Nixon)

Model 2
Model 1
quaker(Nixon) republican(Nixon) ?abnormal1(Nixon)
abnormal2(Nixon)
quaker(Nixon) republican(Nixon) abnormal1(Nixon)
?abnormal2(Nixon)
more preferred to
12
Default Reasoning

• Uncertain reasoning
• car(x) ? wheel-num(x, 4) l1, u2
• bird(x) ? fly(x) l3, u4
• quaker(x) ? pacifist(x) l5, u6
• republican(x) ? ?pacifist(x) l7, u8
• l, u probabilistic or possibilistic intervals