1. 1 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 A: Four (by default) The conclusion is withdrawn if one is supplied with the information that one wheel of John’s car has just been stolen.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

2. 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 A: Yes (by default) The conclusion is withdrawn if it is added that Tweety is a penguin.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. 3 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 A: Four (by default) The conclusion is withdrawn if one is supplied with the information that one wheel of John’s car has just been stolen.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)

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 A: Yes (by default) The conclusion is withdrawn if it is added that Tweety is a penguin.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. 5 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 A: Four (by default - CWA) The conclusion is withdrawn if one is supplied with the information that one wheel of John’s car has just been stolen.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)

6. 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 A: Yes (by default - CWA) The conclusion is withdrawn if it is added that Tweety is a penguin.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. 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. 8 Default Reasoning Usually, Quakers are pacifist Usually, Republicans are not pacifist Richard Nixon is both a Quaker and a Republican Nixon pacifist Quaker Republican Nixon diamond

9. 9 Default Reasoning Usually, Quakers are pacifist Usually, Republicans are not pacifist Richard Nixon is both a Quaker and a Republican quaker(x)   abnormal 1 (x)  pacifist(x) republican(x)   abnormal 2 (x)   pacifist(x) quaker(Nixon) republican(Nixon)

10. 10 Default Reasoning Default consequence: KB  D  iff  is true in every preferred model of KB.

11. 11 Default Reasoning quaker(x)   abnormal 1 (x)  pacifist(x) republican(x)   abnormal 2 (x)   pacifist(x) quaker(Nixon) republican(Nixon) quaker(Nixon) republican(Nixon) abnormal 1 (Nixon)  abnormal 2 (Nixon) … quaker(Nixon) republican(Nixon)  abnormal 1 (Nixon) abnormal 2 (Nixon) … more preferred to Model 1 Model 2

12. 12 Default Reasoning Uncertain reasoning: car(x)  wheel-num(x, 4) [l 1, u 2 ] bird(x)  fly(x) [l 3, u 4 ] quaker(x)  pacifist(x) [l 5, u 6 ] republican(x)   pacifist(x) [l 7, u 8 ] [l, u]: probabilistic or possibilistic intervals