Michael Frazier and Leonard Pitt. CLASSIC learning. Machine Learning, 25:151-- 193, 1996.  Home/Search   Document Details and Download   Summary   Related Articles   Check

....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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M. Frazier, L. Pitt, Classic learning, Mach. Learn. 25(2-3) (1996) 151-193.

....analogous to the settings considered by Angluin, Frazier and Pitt [1992] is also an open area. Finally, much work remains to be done in relating the learnable languages of first order clauses to each other, as well as to other learnable first order languages (e.g. Cohen and Hirsh, 1992; Pitt and Frazier, 1994] Acknowledgments The author would like to thank Haym Hirsh and Rob Schapire for comments on the presentation; Mike Kearns, Jorg Uwe Kietz, and Rob Schapire for a number of helpful discussions; and the reviewers, for their many helpful comments on the presentation and technical content. 35 ....

L. Pitt and M. Frazier. Classic learning. In Proceedings of the Seventh Annual ACM Conference on Computational Learning Theory, Santa Cruz, CA, 1994. ACM Press.

.... logic (DL) and first order horn logic (HL) In Inductive Logic Programming (ILP) learning first order horn logic is investigated in depth, for learning DLs there exist first approaches [ Kietz and Morik, 1994; Cohen and Hirsh, 1994b ] and theoretical learnability results [ Cohen and Hirsh, 1994a; Frazier and Pitt, 1994 ] Recently, it was proposed to use Carin ALN as a framework for learning [ Rouveirol and Ventos, 2000 ] This is an interesting extension of ILP as provides a new bias orthogonal to the one used in ILP, i.e. it allows all quantified descriptions of body variables, instead of the existential ....

Frazier, M. and L. Pitt: 1994, `Classic Learning'. In: Proc. of the 7th Annual ACM Conference on Computational Learning Theory. pp. 23--34.

.... namely description logic (DL) and first order horn logic (HL) In Inductive Logic Programming (ILP) learning first order horn logic is investigated in depth, for learning DLs there exist first approaches and theoretical learnability results [ Kietz and Morik, 1994; Cohen and Hirsh, 1994; Frazier and Pitt, 1994 ] Recently, it was proposed to use Carin ALN as a framework for learning [ Rouveirol and Ventos, 2000 ] This is an interesting extension of ILP as provides a new bias orthogonal to the one used in ILP, i.e. it allows all quantified descriptions of body variables, instead of the existential ....

Frazier, M. and L. Pitt: 1994, `Classic Learning'. In: Proc. of the 7th Annual ACM Conference on Computational Learning Theory. pp. 23--34.

.... namely description logic (DL) and first order horn logic (HL) In Inductive Logic Programming (ILP) learning first order horn logic is investigated in depth, for learning DLs there exist first approaches and theoretical learnability results [ Kietz and Morik, 1994; Cohen and Hirsh, 1994; Frazier and Pitt, 1994 ] Recently, it was proposed to use Carin ALN as a framework for learning [ Rouveirol and Ventos, 2000 ] This is an interesting extension of ILP as provides a new bias orthogonal to the one used in ILP, i.e. it allows all quantified descriptions of body variables, instead of the existential ....

Frazier, M. and L. Pitt: 1994, `Classic Learning'. In: Proc. of the 7th Annual ACM Conference on Computational Learning Theory. pp. 23--34.

....and first order horn logic. In Inductive Logic Programming (ILP) learning first order horn logic is investigated in depth, for learning description logics there exist first approaches [Kietz and Morik, 1994; Cohen and Hirsh, 1994b] and theoretical learnability results [Cohen and Hirsh, 1994a; Frazier and Pitt, 1994] Recently, it was proposed to use CARIN 4 J fl as a framework for learning [Rouveirol and Ventos, 2000] This is a very interesting extension of ILP as 4 Jfprovides a new bias orthogonal to the one used in ILP, i.e. it al lows all quantified descriptions of body variables, instead of the ....

Frazier, M. and L. Pitt: 1994, Classic Learning'. In: Proc. of the 7th Annual A CM Conference on Computational Learning Theory. pp. 23-34.

....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 learnable using EQ and subset queries (SQs) Frazier and Pitt [11] introduced the notion of learning from entailment, and presented that a class of description logic called CLASSIC, a class of labeled DAG, is learnable with EQ and membership queries (MQ) or entailment membership queries, EntMQ) Amoth, Cull, and Tadepalli [3] introduced the into matching ....

....The proofs on the correctness of the generalization operations are straightforward. 3.3 The pruning algorithm The procedure Prune in Fig. 3 handles case (1) and case (2) of Lemma 4 by locally modifying a leaf of t. This pruning algorithm is a descendant of the procedure Prune in Frazier and Pitt [11] to learn description logic and extensively used by Amoth et al. 3] By property (4) of Lemma 2, we can replace the test for the matching relation t v t 3 with the test for the containment L(t) L(t 3 ) using SQ due to the assumption of an infinite alphabet 6. Lemma 5 If an instance t of target ....

M. Frazier, L. Pitt, Classic learning, Machine Learning, 25 (2-3), 151--193, 1996.

.... It can, e.g. be used to introduce the concept of a reactor with cooling jacket by the description Reactor u 9connected to:Cooling Jacket u 8functionality: Vaporize; where Vaporize is a primitive concept (i.e. not further defined) Previous work on how to compute the lcs [ Cohen and Hirsh, 1994; Frazier and Pitt, 1996 ] has concentrated on sub languages of the DL used by the system classic [ Brachman et al. 1991 ] which allows (among other constructors) for value restrictions, but not for existential restrictions. Thus, the main new contribution of the present paper is the treatment of existential ....

....practice. Our method depends on the characterization of subsumption by homomorphisms on description trees, because this allows us to construct the lcs as the product of the description trees. For sub languages of classic, a similar method has been used to construct the lcs [ Cohen and Hirsh, 1994; Frazier and Pitt, 1996 ] even though the characterization of subsumption (via a structural subsumption algorithm [ Borgida and PatelSchneider, 1994 ] is not explicitly given in terms of homomorphisms. The main difference is that these languages do not allow for existential restrictions. The results for simple ....

M. Frazier and L. Pitt. classic learning. Machine Learning, 25, 1996.

....of C CLASSIC. One way to overcome this limitation is to consider algorithms that learn a disjunction of terms rather than a single term. A hypothesis H j H 1 H 2 : Hn then covers an example e (represented as a concept) if and only if 9H i 2 H , e v H i (i.e. H i subsumes e) However, in [FP96] Pitt and Frazier shows that the union of terms of CCLASSIC can subsume a concept even though neither member of the union susbsumes this concept (let us recall that there is no closed world assumption in DLs) Reasoning about the possibility of such interactions makes the problem of learning in ....

M. Frazier and L. Pitt. Classic learning. Machine Learning, 25:151--193, 1996.

....algorithm for ### and a language that allows for concept conjunction and same as, which we will call #. The algorithm for # was extended by Cohen and Hirsh (1994a) to ##### #######, which additionally allows for value restrictions (see (Cohen Hirsh, 1994b) for experimental results) Finally, Frazier and Pitt (1996) presented an lcs algorithm for full #######. ## ####### #### ## ### ######## ####### ###### ### ############ ###### ############ # # # ## ####### # ## ########### #### ##### ##### ### #### ########## ### ### ## ### ###### ## ######### 169 ## ######## ####### 1.2 Total vs. Partial ....

....no longer even exist, and in case it exists its size may grow exponential in the size of the given concept descriptions. Nevertheless, the existence of the lcs of two concept descriptions can be decided in polynomial time. Speci cally, in previous work (Cohen et al. 1992; Cohen Hirsh, 1994a; Frazier Pitt, 1996) concerning the lcs computation in #######, constructions and proofs have been made without realizing the di erence between the two types of attributes. Without going into details here, the main problem for lcs is that merely nite graphs have been employed, making the constructions applicable ....

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Frazier, M., & Pitt, L. (1996). Classic learning. Machine Learning Journal, 25, 151-193.

....statistical software such as SAS STAT contain various forms of regression tools that incrementally postulate and add terms to form functional relations. In relational settings, description logics (sometimes called terminological logics) have been proposed as an extension to first order logic [Frazier and Pitt, 1996] where all but one of the variables are quantified. This allows the expression of predicates such as at least two, at most three, which can be viewed as operating upon the individual original user supplied predicates. Such systems have been used for research into correlating patient symptoms ....

Frazier, M. and Pitt, L. (1996). Classic Learning. Machine Learning, Vol. 25(2--3):pp. 151--193.

.... proof technique may be found by considering a restriction of the (corrected) subsumption algorithm in (Hollunder Nutt, 1990) Description graphs have also turned out to be of interest because they support further theoretical results about DLs, concerning their learnability (Cohen Hirsh, 1994; Pitt Frazier, 1994) results which would seem harder to obtain using the standard notation for DLs. Second, this paper investigates the effect of allowing individuals to appear in descriptions of DLs. As independently demonstrated in (Lenzerini Schaerf, 1991) adding a set description introduces yet another ....

Pitt, L., & Frazier, M. (1994). Classic learning. In Proceedings of the Seventh Annual ACM Conference on Computational Learning Theory New Brunswick, NJ. ACM Press.

....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 example, the algorithm tries to use the example to re ne one of its current clauses. If this succeeds then a new hypothesis is formed by replacing this clause with its re ned version, ....

M. Frazier and L. Pitt. CLASSIC learning. Machine Learning, 25:151-193, 1996.

....system that uses model theory to give a formal base to the representation and reasoning system [6] Most DL learning stu is related with the computation of the Least Common Subsumer (LCS) introduced in [3] as an adaptation of Relative Least General Generalization to the DL eld. See for example [4, 7]. The work of [11] by one hand, and [5] by another, try to acquire a whole theory (using the LCS computation as a subtask) All this DL work, and most ILP one have been done from a concept learning perspective. In this paper I establish a formal framework that addresses the problem of theory ....

M. Frazier and L. Pitt. CLASSIC learning. Machine Learning, 25:151-193, 1996.

....logic programs from examples and queries has attracted a lot of attention in the last fteen years. Many techniques and systems for learning logic programs are developed and used in many applications. See [13] for a survey. In this paper, we consider the framework of learning from entailment [1 5,7,8,15,16] and present a polynomial time algorithm to learn a rich class of logic programs that allow local variables and include many standard programs from Sterling and Shapiro s book [20] This is a revised and extended version of [11] Address for correspondence: M.R.K. Krishna Rao, Institute of ....

M. Frazier and L. Pitt (1994), CLASSIC learning, Proc. COLT'94, pp. 23-34.

.... provide useful information) It can, e.g. be used to introduce the concept of a reactor with cooling jacket by the description Reactoru9connected to:Cooling Jacketu8functionality: Vaporize; where Vaporize is a primitive concept (i.e. not further defined) Previous work on how to compute the lcs [10, 11, 13] has concentrated on sublanguages of the DL used by the system classic [7] which allows (among other constructors) for value restrictions, but not for existential restrictions. Thus, the main new contribution of the present paper is the treatment of existential restrictions. For didactic ....

....not pose a problem in practice. Our method depends on the characterization of subsumption by homomorphisms on description trees, because this allows us to construct the lcs as the product of the description trees. For sub languages of classic, a similar method has been used to construct the lcs [10, 11, 13], even though the characterization of subsumption (via a structural subsumption algorithm [6] is not explicitly given in terms of homomorphisms. The main difference is that these languages do not allow for existential restrictions. The results for simple conceptual graphs and conjunctive queries ....

M. Frazier and L. Pitt. classic learning. Machine Learning, 25:151--193, 1996.

....for ulas. In the beginning of 1990 s, the notion of learning from entailment was intr duced to study thelear55CM 2 y of pr4 ositionalHor sentences [1] 7] and has successfully demonstr8M that varH]4 interC5B8M frC5B ts offir 242M 2 logicar e#cientlylearC2B2 frr entailment [4] 5] [8], 11] 16] 21] 22] Hypothesis constrMC42 techniques developed in ILP play an imp or tantr2H to achieve e#cientlear8CM in theselear488 8 ityr2 #]BM In this paper wetr to combinerneM4B independentlyder2 edfr2 the two r ots with the suppor of moder theorB5 of LogicPrcM4 C 8M In Sect. 2 ....

....appear2C in h (C) and bd(C)ar p and those in # p ,r2C ectively. For definite clauses, the leastgenerC4C]M 42 lg of a set of clauses mayr28H8 in the exponentialbr w up of the size of lg(C, D) To avoid thisprsM4B# we can use an oper245C called pruning (P rune(C) which is or2 ]M 4] intr duced in [8]. Missing(E) Retur E itself. Gen(C,D) Retur P rune(lg(C, D) wher lg is the leastgenerBH22M 24 of a set of clauses. P rune(C) Retur the clause obtainedfra C by deleting thereM2#B] t atoms B # bd(C) whenever H # = h (C) # (bd(C) B ) SQ(C) Use MQ instead of SQ. The ....

M. Frazier and L. Pitt, "Classic learning," Proc. 7th COLT, pp.23--34, 1994.

....be deduced from other boolean variables when # is available. shown to be very useful to reduce the search space explored by a learning procedure. YAYA learning procedure is not involved with PAC learnability nor Least Common Subsumer (LCS) computation [4] as most work in learning DLs does (see [5, 8] for example) Instead, our learning procedure is a general axiom exploration procedure that is heuristically guided by the information theory measures mentioned above. An initial theory ## is evolved # through the addition of new axioms. This is done by the application of a set of ######### ....

M. Frazier and L. Pitt, `CLASSIC learning', ####### ###### ###, ##, 151-193, (1996).

....an instance of a concept. As another reasoning service, the least common subsumer (LCS) operation applied to concepts C and D, computes the most speci c concept which subsumes C and D. The LCS operation is an important reasoning service useful for a number of applications. Cohen, Borgida, Hirsh [3, 6] consider an LCS operation for the description logic ALN including feature chain equalities in order to approximate a disjunction constructor which is not explicitly included in ALN . Baader, K usters Molitor use the operator as a subtask for the bottom up construction of knowledge bases based ....

M. Frazier and L. Pitt. CLASSIC learning. Machine Learning, 1996.

....automata (DFAs) HU79] The Classic description logic is a first order logic used for representing objects and their relationships. A description of Classic is beyond the scope of this paper; we note only that positive results for the learnability of Classic sentences have recently been given [CH94c, CH94b, FP94]. It is helpful to view the example space X n as a lattice with componentwise or and and as the lattice operators. The top element is the vector f1g n and the bottom element is the vector f0g n . The elements are partially ordered by , where x y if and only if for all i, x i y i . If x ....

....is unimportant. Other investigations have considered learning concept classes when membership query responses are incorrect (as opposed to don t know ) Angluin and Krikis [AK94] and Angluin [Ang94] consider learning with a bounded number of such erroneous responses, and Frazier and Pitt [FP94] consider learning when such incorrect responses occur randomly with probability at most 1 2 . In other related work, Kearns and Schapire [KS94] generalized the PAC setting to non binary values using Haussler s framework [Hau89] They define a p concept in which each example x 2 X has some ....

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M. Frazier and L. Pitt. CLASSIC learning. In Proc. 7th Annu. ACM Workshop on Comput. Learning Theory, pages 23--34. ACM Press, New York, NY, 1994. To appear, Machine Learning.

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Michael Frazier and Leonard Pitt. CLASSIC learning. Machine Learning, 25:151-- 193, 1996.

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Michael Frazier and Leonard Pitt. CLASSIC learning. Machine Learning, 25:151-- 193, 1996.

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M. Frazier and L. Pitt. CLASSIC learning. Machine Learning, 25:151-193, 1996.

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M. Frazier, L. Pitt, Classic learning, Machine Learning, 25 (2-3), 151--193, 1996.

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M. Frazier, and L. Pitt, "Classic learning," Proc. 7th COLT, pp.23--34, 1994.

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