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Default Reasoning. Q : How many wheels does John’s car have? A : Four (by default) The conclusion is withdrawn if one is supplied with the information that one wheel of John’s car has just been stolen. non-monotonicity. Default Reasoning. Q : Can bird Tweety fly? A : Yes (by default)

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default reasoning
Default Reasoning

Q: How many wheels does John’s car have?

A: Four (by default)

The conclusion is withdrawn if one is supplied with the information that one wheel of John’s car has just been stolen.

non-monotonicity

default reasoning1
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The conclusion is withdrawn if it is added that Tweety is a penguin.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

default reasoning2
Default Reasoning

Q: How many wheels does John’s car have?

A: Four (by default)

The conclusion is withdrawn if one is supplied with the information that one wheel of John’s car has just been stolen.

car(x)  …  wheel-num(x, 4)

default reasoning3
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The conclusion is withdrawn if it is added that Tweety is a penguin.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)

default reasoning4
Default Reasoning

Q: How many wheels does John’s car have?

A: Four (by default - CWA)

The conclusion is withdrawn if one is supplied with the information that one wheel of John’s car has just been stolen.

car(x)  abnormal(x)  wheel-num(x, 4)

wheel-stolen(x)  abnormal(x)

default reasoning5
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The conclusion is withdrawn if it is added that Tweety is a penguin.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)

default reasoning6
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?

default reasoning7
Default Reasoning

Usually, Quakers are pacifist

Usually, Republicans are not pacifist

Richard Nixon is both a Quaker and a Republican

pacifist

Nixondiamond

Quaker

Republican

Nixon

default reasoning8
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)

default reasoning9
Default Reasoning
  • Default consequence:

KBDa

iff ais true in every preferred model of KB.

default reasoning10
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

default reasoning11
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