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Model Theory – Definite Semantics
- The definite semantics again require a set of conditions to hold
- We can now refer to every formula in E since they are guaranteed to have a truth value in the minimal model
- Consistency:
-
Prior Satisfiability: all
e in E
-
are false in
M
+(
B
)
- Negative evidence should not be part of the minimal model
-
Posterior Satisfiability: all
e in E
-
are false in
M
+(
B
∪
H
)
- Negative evidence should not be supported by our hypotheses
- Completeness
-
Prior Necessity: some
e in E
+
are false in
M
+(
B
)
- If all positive examples are already true in the minimal model of the background knowledge, then no hypothesis we derive will add useful information
-
Posterior Sufficiency: all
e in E
+
are true in
M
+(
B
∪
H
)
- All positive examples are true (explained by the hypothesis) in the minimal model of the background theory and the hypothesis
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