Some Non-First Order Inference
Schemas
| Exceptions: General Axioms are often inadequate.
E.g.: |
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Because
of exceptions, the general axiom that states that if x is
a bird then x flies leads to an inconsistency as illustrated
in the axioms to the left.
An alternative is to throw out
the general axiom and explicitly list the exceptions as illustrated
below:
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| |
 |
| However, other exceptions
come to mind...what if a wing is broken, what if an oil spill
has covered the bird, what if the bird is still too young to
fly, ....etc. The fact that we can come up with so many exceptional
conditions, makes us suspect that there isn't a closed set of
exceptions. Perhaps, first order axioms are simply not the way
to capture this type of knowledge. |
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Frame
Problem:
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| In
a changing world there is a need to represent those aspects of
the world that remain invariant under certain state changes.
E.g., Painting an object will not affect the location of any
objects. |
|
Frame Axiom:
Assume that every action leaves
every relation unaffected unless it is possible to deduce otherwise.
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| Negation
From Failure |
| e.g., Airline Table, if you fail to find
a flight between city a and city b then infer that there is none. |
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| All
of these examples are non-first order schemes of inference! |
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