Hiroki Arimura. Learning acyclic rst-order Horn sentences from entailment. In Proceedings of the International Conference on ALT, Sendai, Japan, 1997. Springer-Verlag. LNAI 1316.  Home/Search   Document Not in Database   Summary   Related Articles   Check

....of Horn expressions in rst order logic but the picture there is less clear. Except for a monotone like case [24] the query complexity is either exponential in one of the crucial parameters (e.g. universally quanti ed variables) 17, 4] or the algorithms use additional syntax based oracles [5, 25]. It is thus interesting to investigate whether this gap is necessary. The current paper takes a rst step in this direction by studying the query complexity in the propositional case. Query complexity can be characterized using the combinatorial notion of polynomial certi cates [14, 12] see ....

Hiroki Arimura. Learning acyclic rst-order Horn sentences from entailment. In Proceedings of the International Conference on ALT, Sendai, Japan, 1997. Springer-Verlag. LNAI 1316.

....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, ....

.... the algorithm in [10, 11] uses direct products of models we use an operation based on the lgg (least general generalisation [17] The use of lgg seems a more natural and intuitive technique to use for learning from entailment, and it has been used before, both in theoretical and applied work [3, 20, 19, 14]. The class of Closed Horn Expressions shown to be learnable here, includes both the class of Range Restricted Horn Expressions, the class of Constrained Horn Expressions and their union . In addition, the complexity of the algorithm is better than that of the algorithm in [10, 11] We extend ....

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Hiroki Arimura. Learning acyclic rst-order Horn sentences from entailment. In Proceedings of the International Conference on ALT, Sendai, Japan, 1997. Springer-Verlag. LNAI 1316.

....xRy and yRz ) xRz) Let hG; i be a quasi ordered set and let x; y 2 G. If x y and there is no z such that x z y, then x is an upward cover of y, and y is a downward cover of x. subsumption is a quasi order that is usually de ned between clauses, but has also been de ned between theories [1, 3]: De nition 1. subsumption) A clause c 1 subsumes a clause c 2 (c 1 c 2 ) i c 1 c 2 . Two clauses c 1 and c 2 are equivalent (c 1 c 2 ) i c 1 c 2 and c 2 c 1 . A clause c 1 is reduced i there is no proper subset c 2 of c 1 (c 2 c 1 ) such that c 1 c 2 . A theory T 1 ....

H. Arimura. Learning acyclic rst-order horn sentences from entailment. In Proc. of ALT-97, LNAI 1316, pp. 432-445. Springer-Verlag, 1997.

....(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 ....

....the concept being learned. Several forms of examples (i.e. atoms, clauses, interpretations) have been used before in ILP [7] and each of these yields a di erent learning model when combined with the query setting. Some authors use additional query types to allow for more ecient learning. Arimura [4] and Reddy and Tadepalli [22] used derivation order queries to identify 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 ....

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H. Arimura. Learning acyclic rst-order Horn sentences from entailment. In Proceedings of the International Conference on Algorithmic Learning Theory, Sendai, Japan, 1997. Springer-verlag. LNAI 1316.

....append, merge, split, delete, member, prefix, suffix, length, reverse, append 4 on lists, tree traversal programs on binary trees and addition, multiplication and exponentiation on natural numbers. Grafting a few aspects of incremental learning [10] onto the framework of learning from entailment [3], we generalize the existing results to allow local variables, which play an important role of sideways information passing in the paradigm of logic programming. 1 Introduction Starting with the seminal work of Shapiro [18,19] the problem of learning logic programs from examples and queries has ....

....of learning from entailment has been introduced by Angluin [1] and Franzier and Pitt [7] to study learnability of propositional Horn sentences. In the last few years, this framework (with minor modi cations) has been used in learning rst order Horn programs and many results have been published in [3,11,16]. In [3,11,16] the learner is allowed to ask the following types of queries in learning a concept (logic program) from a teacher. Through an entailment equivalence query EQUIV (H) the learner asks the teacher whether his program H is logically equivalent to the target program H or not. The ....

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H. Arimura (1997), Learning acyclic rst-order Horn sentences from entailment, Proc. of Algorithmic Learning Theory, ALT'97, Lecture Notes in Articial intelligence 1316, pp. 432-445.

....We also allow a learner to use two types of additional queries for the target EFS H . The rst type of queries is the entailment membership query in the model of the learning from entailment [15, 31] This model is considered to be reasonable for learning the rstorder logic or logic programs [10, 11, 16, 19, 31]. The goal of a learning algorithm is to nd a hypothesis equivalent to the target hypothesis w.r.t. the entailment semantics using the queries. The entailment semantics is de ned in the next section together with other semantics. The second type of queries is the dependency query to determine ....

....in a dependency relation. We design a learning algorithm for THEFS( k; r) with equivalence, entailment membership, and dependency queries. This algorithm adopts the bottom up search strategy by combining three generalization techniques, namely, saturation, rewind and maximal common subsumer [10, 11, 15, 16, 19, 31]. We show that for every k; r 0, this algorithm exactly learns the class THEFS( k; r) in polynomial time using O(pmn ) equivalence queries, O(p ) entailment membership queries, and O(p dependency queries, where m is the number of clauses and n is the length of the ....

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H. Arimura, Learning acyclic rst-order Horn sentences from entailment, in: Proc. 8th Internal. Workshop on Algorithmic Learning Theory, LNAI 1316 (SpringerVerlag, 1997) 432-445.

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