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sav08:deciding_quantifier-free_fol [2008/04/17 13:23] vkuncak |
sav08:deciding_quantifier-free_fol [2008/04/17 13:33] vkuncak |
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Recall [[Herbrand Universe for Equality]]. | Recall [[Herbrand Universe for Equality]]. | ||
- | What can we assume about the domain of interpretations of $a,b,f$? | + | What can we assume about the domain of interpretations of $a,b,f$? ++ | they are interpreted over elements of factor structure of ground terms ++ |
Recall [[Axioms for Equality]]. | Recall [[Axioms for Equality]]. | ||
+ | |||
+ | Suppose that there exists a model. What do we know about the congruence? | ||
The family of all congruences that contain a given relation. | The family of all congruences that contain a given relation. | ||
Closure under intersection. | Closure under intersection. | ||
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+ | Existence of smallest congruence containing a given relation. | ||
Iterative algorithm for finding congruence closure. | Iterative algorithm for finding congruence closure. | ||
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