Default Reasoning

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# Default Reasoning - PowerPoint PPT Presentation

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 A : Four (by default) The conclusion is withdrawn if one is supplied with the information that one wheel of John’s car has just been stolen.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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Presentation Transcript
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The conclusion is withdrawn if one is supplied with the information that one wheel of John’s car has just been stolen.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)

The conclusion is withdrawn if it is added that Tweety is a penguin.

non-monotonicity

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The conclusion is withdrawn if one is supplied with the information that one wheel of John’s car has just been stolen.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 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The conclusion is withdrawn if it is added that Tweety is a penguin.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 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The conclusion is withdrawn if one is supplied with the information that one wheel of John’s car has just been stolen.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 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The conclusion is withdrawn if it is added that Tweety is a penguin.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 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 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 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 Reasoning
• Default consequence:

KBDa

iff ais true in every preferred model of KB.

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 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