H. Arimura, H. Ishizaka, T. Shinohara, S. Otsuki, A generalization of the least general generalization, Machine Intelligence, 13, 59--85, 1994.  Home/Search   Document Details and Download   Summary   Related Articles   Check

....see Amoth, Cull and Tadepalli [3] The study of tree patterns is motivated by natural language processing [15] and symbolic integration [34] where instances are represented as parse trees and expressions [34] respectively. Tree patterns are also closely related to logic program representations [10, 23]. Using the exact learning model with membership and equivalence queries, Arimura, Ishizaka and Shinohara [11] showed that ordered forests with bounded number of trees can be learned eciently. Subsequently, Amoth, Cull and Tadepalli [2] showed that ordered forests with an in nite alphabet are ....

H. Arimura, H. Ishizaka, T. Shinohara, and S. Otsuki. A generalization of the least general generalization. In Machine Learning, volume 13, pages 59-85. Oxford Univ. Press, 1994.

....under a ranked alphabet are called unions of tree patterns in [7] Definition 8. For an ordered gapped forest H, we define the language of H with the into semantics as the union L in (H) t2H L in (t) of the languages defined by its members. The following property is called the compactness [3, 2, 6, 8] and plays an important role in the learning of unions of languages [8] Lemma 6. Let 6 be an infinite alphabet. For any ordered gapped forests P;Q 2 OGF , L in (P ) L in (Q) if and only if for every q 2 Q there exists some p 2 P such that p w q. Algorithm LEARN INTO LIN OGT BY SQ Given: ....

H. Arimura, H. Ishizaka, T. Shinohara, S. Otsuki, A generalization of the least general generalization, Machine Intelligence, 13, 59--85, 1994.

....unordered forests with the into match semantics as unions (sets) of patterns in OGT. Learning of tree patterns dates back to Plotkin [17] where OT with the onto semantics considered and shown to be polynomial time learnable from examples or equivalence query (EQ) alone. Arimura et al. [7] extended Plotkin s algorithm for bounded number of ordered forests. Page and Frisch [16] showed that a class of OT with background theory is polynomial time learnable by a similar algorithm. Arimura et al. 8] and Amoth et al. 4] showed that ordered forests OF with the onto semantics is ....

H. Arimura, H. Ishizaka, T. Shinohara, S. Otsuki, A generalization of the least general generalization, Machine Intelligence, 13, 59--85, 1994.

....this sequence will eventually converges to H . To ensure the convergence, we use an approximation Delta v Delta of M( Delta) M( Delta) defined as follows. We extend the subsumption relation for ordered equations to the relation w for sets of ordered equations. Definition 10 (Arimura et al.[3]) Let P; Q be sets of rewriting rules. Then, we define P v Q iff for any C 2 P , there exists some D 2 Q such that C D. We say that Q is a generalization of P , or P is a refinement of Q. If P v Q but Q 6v P then we define P Q. Lemma 2. P v Q implies M(P ) M(Q) Proof. Since M(Q) is closed ....

H. Arimura, H. Ishizaka, T. Shinohara, S. Otsuki, "A generalization of the least general generalization, " Machine Intelligence, vol.13, pp.59--85, Oxford University Press, 1994.

....is unique, of polynomial size and polynomial time computable [17] Then, if the examplesar unit clauses, the unknown clause H is given by the leastgener45HBM 2] of S. Ar4 ur et al..gener4 M H this concept when therar mor than one unknown hypotheses, and defined multiple minimal generalization [3]. Gener4]8M H#H2 of a set of clauses S and its least gener42]BM HB (denoted also by lg(S) ar defined in the same way (Sect. 5.3) We can use this method to select anapprB#M HH hypothesisfre the possible candidatesgenersM2 frer e.g. satur4 tgenerM H 2#5Mr and toincor oror a newly obtained ....

....is defined as P # Q i#for any C # P , ther exists some D # Q such that C # D.Wesay that Q is a generalization of P,or P is a refinement of Q.IfP # Q but Q ## P then we define P # Q. ClearC Q # P implies P = Q, but the conver] does not hold ingenerC# Definition 18 ([3]) Ar4 ]44M t P of Q is said to be conservative iffor any D # Qther is at most one C # P such that C # D. Next, we discuss how to update Hnfr5 a given counter2HC55M En.IfP is always aconser ativerC finement of H # then any En # U is positive. Then, the firM task is tor2BC2#M HC fr2 ....

H. Arimura, H. Ishizaka, T. Shinohara, and S. Otsuki, "A generalization of the least general generalization," Machine Intelligence, vol.13, pp.59--85, Oxford University Press, 1994.

....a nonnegative integer k, TP k is the class of sets of at most k tree patterns. Although concepts in TP k are simple, they have characteristics common to a variety of representation frameworks for structured objects such as knowledge representation languages [7, 10] logic programming languages [6, 13], and combinatorial objects like string patterns [1, 3, 5, 9] Furthermore, computational problems related to tree patterns are more efficiently solvable than the other representation frameworks; for example, the membership and the containment problems are polynomial time solvable for tree ....

H. Arimura, H. Ishizaka, T. Shinohara, and S. Otsuki. A generalization of the least general generalization. Machine Intelligence, 13, 59--85, Oxford Univ. Press, 1994.

Online articles have much greater impact   More about CiteSeer.IST   Add search form to your site   Submit documents   Feedback  

CiteSeer.IST - Copyright Penn State and NEC