We study the learnability of first order Horn expressions from equivalence and membership queries. We show that the class of expressions where every term in the consequent of a clause appears also in the antecedent of the clause is learnable. The result holds both for the model where interpretations are examples (learning from interpretations) and the model where clauses are examples (learning from entailment).
The result for learning from interpretations is derived by exhibiting a reduction to the function free case (which was previously shown to be learnable). The reduction uses flattening of clauses - replacing a function symbol with a predicate symbol of arity larger by one - and an axiomatisation of the functionality of the new predicates. Learning from entailment is then shown possible by reducing it to learning from interpretations under the given restrictions. This relies on a procedure for model finding for this class. We also motivate the choice of restriction by showing that for such expressions implication is decidable. Hence, the learned expressions can be used as a knowledge base in a system in a useful way.ECS-LFCS-98-395.
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