R. Khardon. Learning range restricted Horn expressions. In Proceedings of the Fourth European Conference on Computational Learning Theory, pages 111--125, Nordkirchen, Germany, 1999. Springer-verlag. LNAI 1572.  Home/Search   Document Details and Download   Summary   Related Articles   Check

....their researches by Cohen [5, 6, 7, 9] Dzeroski [10, 12, 23] Kietz [22, 23, 24] and Page [9, 27] have placed the theoretical researches for the learnability of logic programs in one of the main research topics in inductive logic programming. Recently, it has deeply developed by many researchers [1, 20, 25, 26, 30, 31]. On the other hand, a conjunctive query problem in relational database theory [2, 4, 14, 17, 35] is a problem to determine whether or not a tuple belongs to the answer of a conjunctive query over a database. Here, a tuple, a conjunctive query, and a database in 1 relational database theory are ....

....adopted both the simple instance [7] and the extended instance [5, 6] If the extended instance is allowed, then many programs that are usually written with function symbols can be rewritten as function free programs. There is also a close relationship between extended instances and flattening [10, 18, 26, 32]. Some experimental learning systems such as Foil [29] also impose a similar restriction. See the papers [5, 6] for more detail. In the following, we introduce some definitions and notions of learning theory. Let X be a set, called a domain. Define a concept c over X to be a representation of some ....

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R. Khardon, Learning range-restricted Horn expressions, in: Proc. 4th Euro. Conf. on Computational Learning Theory, LNAI 1572 (Springer, 1999) 111--125.

....of a clause appear in the antecedent of the clause, possibly as subterms of more complex terms. This work is based on previous results on learnability of function free Horn expressions and range restricted Horn expressions. The problem of learning range restricted Horn expressions was solved in [Kha99b] by reducing it to the problem of learning function free Horn expressions, solved in [Kha99a] The algorithm presented here has been obtained by retracing this reduction and using the resulting algorithm as a starting point. However, it has been significantly modified and improved. The algorithm ....

....by reducing it to the problem of learning function free Horn expressions, solved in [Kha99a] The algorithm presented here has been obtained by retracing this reduction and using the resulting algorithm as a starting point. However, it has been significantly modified and improved. The algorithm in [Kha99a,Kha99b] uses two main procedures. The first, given a counterexample clause, minimises the clause while maintaining it as a counterexample. The minimisation procedure used here is stronger, resulting in a clause which includes a syntactic variant of a target clause as a subset. The second procedure ....

[Article contains additional citation context not shown here]

R. Khardon. Learning range restricted Horn expressions. In Proceedings of the Fourth European Conference on Computational Learning Theory, pages 111--125, Nordkirchen, Germany, 1999. Springer-verlag. LNAI 1572.

....(A) 11780284. of their researches, Cohen [5 7, 9] Dzeroski [11, 12, 21] Kietz [20 22] and Page [9, 26] have placed the theoretical researches for the learnability of logic programs in one of the main research topics in inductive logic programming. Recently, it has been deeply developed as [1, 18, 23, 24, 29, 30]. On the other hand, a conjunctive query problem in relational database theory [2, 4, 14, 16, 34] is a problem to determine whether or not a tuple belongs to the answer of a conjunctive query over a database. Here, a tuple, a conjunctive query, and a database in relational database theory are ....

....adopted both the simple instance [7] and the extended instance [5, 6] If the extended instance is allowed, then many programs that are usually written with function symbols can be rewritten as function free programs. There is also a close relationship between extended instances and flattening [10, 17, 24, 31]; Some experimental learning systems such as Foil [28] also impose a similar restriction. See the papers [5, 6] for more detail. In the following, we introduce some definitions and notions of learning theory. Let X be a set, called a domain. Define a concept c over X to be a representation of some ....

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Khardon, R.: Learning range-restricted Horn expressions, Proc. EuroCOLT99, LNAI 1572, 111--125, 1999.

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R. Khardon. Learning range restricted Horn expressions. In Proceedings of the Fourth European Conference on Computational Learning Theory, pages 111--125, Nordkirchen, Germany, 1999. Springer-verlag. LNAI 1572.

No context found.

R. Khardon. Learning range restricted Horn expressions. In Proceedings of the Fourth European Conference on Computational Learning Theory, pages 111--125, Nordkirchen, Germany, 1999. Springer-verlag. LNAI 1572.

....Frazier Pitt [6] formalised learning from entailment using equivalence queries and membership queries and showed the learnability of propositional Horn expressions. Generalising this result to the rst order setting is of clear interest. Indeed, several works have been done following this line [9, 3, 20, 19, 10, 11, 2] obtaining algorithms that work for certain subsets of Horn expressions. Learning rst order Horn expressions has become a fundamental problem in Inductive Logic Programming [15] Theoretical results have shown that learning from examples only is feasible for very restricted classes [4] and that, ....

....and membership queries (MIS [23] CLINT [18] for example) Some of the techniques developed in this framework have been adapted for systems that learn from examples only [21, 12] We present an algorithm to learn certain subsets of Horn expressions. The algorithm is related to the ones in [10, 11], which learn Range Restricted Horn expressions. The algorithms in [10, 11] and here use two main procedures. The rst, given a counterexample clause, minimises the clause while maintaining it as a counterexample. The minimisation procedure used here is stronger than those in [10, 11] resulting in ....

[Article contains additional citation context not shown here]

R. Khardon. Learning range restricted Horn expressions. In Proceedings of the Fourth European Conference on Computational Learning Theory, pages 111-125, Nordkirchen, Germany, 1999. Springer-verlag. LNAI 1572.

....(e.g. 20, 17, 9, 5] Since only limited classes of expressions are learnable from examples [6] heuristics are used to obtain good results in practice. One recent strand of theoretical work has shown that larger classes of expressions are learnable if the learner is allowed to ask questions [12, 21, 4, 22, 16, 14, 13, 3, 15]. These works use standard oracles from learning theory [1] as well as new types of questions appropriate for the rst order setting. Two main challenges remain in this area. One is to further clarify which classes are learnable and with what complexity. The other is to establish applications of ....

....which atom is the rst one to be used when deriving a particular conclusion. Krishna Rao and Sattar [16] use subsumption queries to nd out whether hypothesised clauses syntactically match the concept being learned. Despite the variation in example types and question types the algorithms in [12, 21, 4, 22, 16, 14, 13, 3] share a common structure, which is already re ected in learning propositional expressions [1, 2, 10] A similar structure is used for learning description logic expressions in [11] The algorithms maintain multi clause hypotheses, and learn all clauses simultaneously. Given a new uncovered ....

R. Khardon. Learning range-restricted Horn expressions. In Proceedings of the Fourth European Conference on Computational Learning Theory, pages 111-125, Nordkirchen, Germany, 1999. Springer-verlag. LNAI 1572.

No context found.

Khardon, R. (1999b). Learning range-restricted Horn expressions. Proceedings of the European Conference on Computational Learning Theory (pp. 111--125). LNAI 1572.

....appear in the antecedent of the clause, possibly as subterms of more complex terms. This work is based on previous results on learnability of function free Horn expressions and range restricted Horn expressions. The learnability of the class of range restricted Horn expressions was solved in [Kha99b] by reducing it to the case of function free Horn expressions, already solved in [Kha99a] The algorithm presented here has been obtained by retracing this reduction and using the resulting algorithm as a starting point. However, it has been significantly modified and improved. The algorithm in ....

....by reducing it to the case of function free Horn expressions, already solved in [Kha99a] The algorithm presented here has been obtained by retracing this reduction and using the resulting algorithm as a starting point. However, it has been significantly modified and improved. The algorithm in [Kha99a, Kha99b] uses two main procedures. The first, given a counterexample clause, minimises the clause while maintaining it as a counterexample. The minimisation procedure used here is stronger resulting in a clause which includes a syntactic variant of a target clause as a subset. The second procedure ....

[Article contains additional citation context not shown here]

R. Khardon. Learning range restricted Horn expressions. In Proceedings of the Fourth European Conference on Computational Learning Theory, pages 111--125, Nordkirchen, Germany, 1999. Springer-verlag. LNAI 1572.

....as subterms of more complex terms. And every clause includes in its antecedent all inequalities possible between all terms appearing in it. The paper shows that small modifications to the algorithm and proof of [AK00] yield the learning result. Further background and related work appear in [Ari97, RT98, RS98, MF92, Kha99a, Kha99b]. The rest of the paper is organised as follows. Section 2 gives some preliminary definitions. The learning algorithm is presented in Section 3 and proved correct in Section 4. 2 Preliminaries 2.1 Inequated Range Restricted Horn Expressions We consider a subset of the class of universally ....

R. Khardon. Learning range restricted Horn expressions. In Proceedings of the Fourth European Conference on Computational Learning Theory, pages 111--125, Nordkirchen, Germany, 1999. Springer-verlag. LNAI 1572.

....on function free expressions, extending the results to more expressive languages in clearly of interest. One such result for range restricted Horn expressions (where the way function symbols are used in clauses is restricted) has been recently developed using a reduction to the function free case (Khardon, 1998). The rest of the paper is organised as follows. Section 2 gives preliminary definitions and details. Section 3 presents some simple examples that motivate the construction developed in Section 4 where the result on learning with the special semantics is proved. Section 5 extends this result for ....

....in the sense that computations with them are decidable and efficient. Some progress in this direction was recently made, showing that a natural generalisation of range restricted expressions, where every term that appears in the consequent of a clause also appears in its antecedent, is learnable (Khardon, 1998). Acknowledgements A preliminary version of this paper appeared in COLT 1998. This work was partly supported by EPSRC Grant GR M21409. Part of this work was done while the author was at Harvard University and supported by ARO grant DAAL03 92 G 0115 and ONR grant N00014 95 1 0550. I am grateful ....

Khardon, R. (1998). Learning range-restricted Horn expressions. Tech. rep. ECS-LFCS98 -395, Laboratory for Foundations of Computer Science, Edinburgh University.

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IOS Press. Khardon, R. (1999a). Learning range-restricted Horn expressions. In Proceedings of the Fourth European Conference on Computational Learning Theory, pp.

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