Reddy, C. and Prasad Tadepalli. 1997. Learning horn definitions with equivalence and membership queries. In S. Dzeroski and N. Lavrac, editors, Proceedings of the 7th International Workshop on Inductive Logic Programming, volume 1297, pages 243-- 255. Springer.  Home/Search   Document Details and Download   Summary   Related Articles   Check

....for learning first order formulas, in which examples are formulas in the firstorder language which are implied or not implied. In this framework, a number of efficient learnability results are obtained for various fragments of first order logic have been shown to be learnable using this framework [1, 4, 9 12, 15, 16]. Recently, it is found that a class of learning algorithms for subclasses of first order Horn programs has a common scheme [16, 22] which has its origin in a monotone Boolean DNF learner in [18] Reddy and Tadepalli [16] proposed an algorithm with subsumption membership queries and saturation ....

.... [19, 21] They have demonstrate that known efficient learnability results for several fragments of first order Horn sentences can be derived from this generic algorithm by appropriately selecting specific procedures for inverting resolution: unit clause programs[4] non recursive Horn definitions [15], constrained atoms with acyclic background theory[12] propositional Horn sentences[9] constrained acyclic Horn programs[4] and acyclic Horn programs [16] In this paper, we apply this framework based on the proof completion to polynomial time learning of functions over labeled trees expressed ....

C. Reddy and P. Tadepalli, "Learning Horn definitions with equivalence and membership queries," Proc. the seventh ILP workshop (LNAI 1297), pp.243--255, 1997.

.... 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 we give ....

....is of k variable if any C # H contains at most k distinct varB55HM The arity of H is the maximumar] y of its pr C424M Definition 15 ( 16] C is constrained if everter occur5M in bd(C) is also asubter of anarHH#] t of h (C) H is constr8 BH if so ar all C # H . Definition 16 ( 4] [21]) H is acyclic ifther exists a terHBBM #] rrHBB over atoms such thath (C) B holdsfor all instances C of clauses in H and all B # bd(C) For ever k # 0, we denote by ACH(k) the class of all definitepriteM H thatar acyclic,constrMHH#2 and ofar# y k.IfH is in ACH(k) then D # C and ....

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C. Reddy and P. Tadepalli, "Learning Horn definitions with equivalence and membership queries," Proc. 7th International Workshop on Inductive Logic Programming (LNAI 1297), pp.243--255, 1997.

....were derived (Shapiro, 1991; De Raedt Bruynooghe, 1992) More recently progress has been made on the problem of learning first order Horn expressions from equivalence and membership queries. These results were obtained by using additional constraints on 2 KHARDON the language (Page, 1993; Reddy Tadepalli, 1997) and using additional queries that help identify the syntactic form of the target expression (Arimura, 1997; Reddy Tadepalli, 1998; Rao Sattar, 1998) In this paper we show that function free universally quantified Horn expressions are exactly learnable in several models of learning from ....

....if the algorithm replaces s i with a pairing of the same size then it may be tricked into an infinite loop: by using I 3 = I 1 we get that s 2 1 Omega I 3 is isomorphic to s 1 1 Omega I 2 . LEARNING HORN EXPRESSIONS 17 It is interesting to note that T in this example is a Horn definition (Reddy Tadepalli, 1997) since both clauses have the same consequent. The algorithm of Reddy and Tadepalli (1997) learns this class and uses least general generalisations which are similar to products. Their algorithm uses a finer minimisation step removing one atom at a time from a clause (in contrast to removing all ....

[Article contains additional citation context not shown here]

Reddy, C., & Tadepalli, P. (1997). Learning Horn definitions with equivalence and membership queries. In International Workshop on Inductive Logic Programming, pp. 243--255 Prague, Czech Republic. Springer. LNAI 1297.

.... In the relational domain, queries have been used in several systems (e.g. Shapiro, 1983; Sammut Banerji, 1986; De Raedt Bruynooghe, 1992; Muggleton Buntine, 1992) and results on learnability in the limit were derived for some (e.g. Shapiro, 1983; De Raedt Bruynooghe, 1992) More recently Reddy and Tadepalli (1997, 1998) considered the use of equivalence and membership queries and have shown that Horn definitions (where all clauses have the same unique positive literal) and acyclic Horn expressions are learnable. In this paper we show that function free universally quantified Horn expressions are exactly ....

....bounded by a constant a then the size of the extension of an example is polynomial in the number of domain elements. Examples of this form have been used by Haussler (1989) and are motivated by the scenario of acting in structural domains (e.g. Khardon, 1996; Reddy, Tadepalli, Roncagliolo, 1996; Reddy Tadepalli, 1997). They are also used in the non monotonic form of ILP (De Raedt Dzeroski, 1994) In structural domains, domain elements are objects in the world and an instantiation describes properties and relations of objects. We therefore refer to domain elements as objects. For convenience we assume a ....

[Article contains additional citation context not shown here]

Reddy, C., & Tadepalli, P. (1997). Learning Horn definitions with equivalence and membership queries. In International Workshop on Inductive Logic Programming, pp.

.... several systems [Sha83,SB86,DRB92,MB92] and results on learnability in the limit were derived [Sha91,DRB92] More recently progress has been made on the problem of learning first order Horn expressions from equivalence and membership queries using additional constraints or other additional queries [Ari97,RT97,Kha98,RT98,RS98]. This work was partly supported by EPSRC Grant GR M21409. In particular [Kha98] shows that universally quantified function free Horn expressions are exactly learnable in several models of learning from equivalence and membership queries. This paper extends these results to a class of ....

....Learning from entailment [FP93] where examples are clauses in the language is defined in Section 5. An example is an interpretation; an example I is positive for a target expression T if I j= T and negative otherwise. Examples of this form have been used before by various authors including [Hau89,DRD94,RT97,Kha98]. We use Angluin s model of learning from Equivalence Queries (EQ) and Membership Queries (MQ) Ang88] Let H be a class under consideration, H a (possibly different) class used to represent hypotheses, and let T 2 H be the target expression. For membership queries, the learner presents an ....

C. Reddy and P. Tadepalli. Learning Horn definitions with equivalence and membership queries. In International Workshop on Inductive Logic Programming, pages 243--255, Prague, Czech Republic, 1997. Springer. LNAI 1297.

.... are known to be learnable in polynomial time from equivalence and membership queries [AFP92, FP93] In the relational domain, queries have been used in several systems [Sha83, SB86, DRB92, MB92] and results on learnability in the limit were derived [Sha83, DRB92] More recently Reddy and Tadepalli [RT97, RT98] considered the use of equivalence and membership queries and have shown that Horn definitions (where all clauses have the same unique positive literal) and acyclic Horn expressions are learnable. In previous work [Kha98] we have shown that universally quantified function free Horn expressions ....

....each predicate symbol p 2 P of arity n, I specifies the truth values of p on n tuples over D. The extension of a predicate in I is the set of positive instantiations of it that are true in I. Let str(S) be the set of interpretations for the signature S Examples of this form have been used in [Hau89, RT97, Kha98] and are motivated by the scenario of acting in structural domains (e.g. Kha96, RTR96] They are also used in the non monotonic form of ILP [DRD94] In structural domains, domain elements are objects in the world and an instantiation describes properties and relations of objects. We therefore ....

C. Reddy and P. Tadepalli. Learning Horn definitions with equivalence and membership queries. In International Workshop on Inductive Logic Programming, pages 243--255, Prague, Czech Republic, 1997. Springer. LNAI 1297.

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Reddy, C. and Prasad Tadepalli. 1997. Learning horn definitions with equivalence and membership queries. In S. Dzeroski and N. Lavrac, editors, Proceedings of the 7th International Workshop on Inductive Logic Programming, volume 1297, pages 243-- 255. Springer.

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