N. Helft, Inductive generalization: a logical framework. in: Progress in Machine Learning, I. Bratko and N. Lavra c, eds, Sigma Press, 1987, 149--157.  Home/Search   Document Not in Database   Summary   Related Articles   Check

.... For given m and n, such a procedure returns an hypothesis made up of m literals bond(X i ,X j ) and involving n variables, where the variables X i and X j in each literal are randomly selected among n variables 1 , X n in such a way that X i X j and the overall hypothesis is linked [6]. The cases in which n m 1 were not considered, since it is not possible to build a clause with m binary literals that contains more than m 1variables and that fulfills the linkedness constraint imposed by the previously described construction method. Specifically, for each (m, n) pair (1 m ....

N. Helft. Inductive generalization: A logical framework. In I. Bratko and N. Lavra c, editors, Progress in Machine Learning, pages 149--157, Wilmslow, UK, 1987. Sigma Press.

....A= a 1 , a 2 , a l a set of Datalog atoms. Conjunctions of atoms on A are called atomsets [5] In our framework, the language of patterns L is the set of well formed atomsets generated on A. Necessary conditions for an atomset P to be in L are the presence of the key atom, the linkedness [13], and the safety. In particular, the last property guarantees the correct evaluation of patterns when they require the handling of negation (see Example 2) To a pattern P we assign an existentially quantified conjunctive formula eqc(P) obtained by turning P into a Datalog query. Definition A ....

Helft, N.: Inductive generalization: a logical framework. In: Bratko, I., Lavrac, N. (eds): Progress in Machine Learning. Sigma Press (1987) 149-157

....match a description that contains the chemically senseless literals atm(d191, d191 18, c, 21, 0.002) bond(d191, d191 18, d191 18, 1) and bond(d191, d191 18, d191 18, 2) Of course, the PROGOL clause can be made more specific by adding inequalities for the variables. This is for example done in [13], but leads to an extreme computational overhead, e.g. when evaluating clauses during hypothesis construction and when constructing the lgg. Therefore, in TRITOP the atoms of a compound are represented using node variables which cannot by definition be instantiated with the same value. The ....

....can be regarded as an extension of Haussler s most specific generalization (msg) for existential conjunctive expressions ( 12] to N ary concepts. In [18] J. U. Kietz investigated the relation between Haussler s msg and the msg for clauses with so called difference links defined by Helft ([13]) Helft s most specific generalization is based on Plotkin s lgg and uses explicit inequalities between variables. Kietz showed in [18] that Helft s msg can be seen as the union of all Haussler msg s. He also shows that the complexity of constructing the Haussler msg from the Helft msg is ....

N. Helft. Inductive generalization: A logical framework. In Proceedings of the Second Working Session on Learning, pages 149--157, 1987.

....L class that e.g. minimizes the expected classification error. In this paper, we will use a sorted logical language L ex to represent relational structures in a graph theoretical manner. Nodes are represented by variables of the sort node. As in (Vere, 1975) and similar to the approach of Helft (Helft, 1987) different node variables are assumed to denote different objects in the described domain which is not the case in the standard semantics of first order logic. In many application domains, this approach produces more intuitive results. In section 2 we give a formal model for this approach that ....

....; x 3 ) d(x 1 ; x 2 ) with node variables x 1 ; x 2 ; x 3 the less general attribute Phi(A) class(x 1 ; x 2 ; y) s(x 1 ; x 3 ) s(x 2 ; x 3 ) d(x 1 ; x 2 ) x 1 = x 2 , x 2 = x 3 , x 1 = x 3 whose inequalities enforce x 1 , x 2 and x 3 to be bound to different objects. In contrast to (Helft, 1987) we will handle the inequalities implicitly in algorithms. Subsumption is used to compare the generality of attributes and to check, if an attribute occurs in a classified object. A clause C 1 subsumes a clause C 2 C 1 C 2 if C 1 C 2 holds for a substitution . A clause C 1 ff ....

Helft, N. (1987). Inductive generalization: A logical framework. In: Proceedings of the Second Working Session on Learning. pp. 149--157.

....natural in many, e.g. technical application domains. To compare the generality of clauses in this framework, we will introduce an alphabetical subsumption relation (ff subsumption) that relies on alphabetical substitutions (ff substitutions) and preserves the distinctness of node variables. In [5], N. Helft uses inequalities to express the distinctness of variables. Though we also use inequalities for defining the meaning of clauses containing node variables, we propose a different notion of least generalization. In contrast to Plotkin s (and Helft s) least generalization (lgg, see [10] ....

N. Helft. Inductive generalization: A logical framework. In Proceedings of the Second Working Session on Learning, pages 149--157, 1987.

....can be found. 4. Assign p i 1 = p i n fLjL 2 c i g 5. If p i 1 = OE then assign n = i and stop, otherwise increase i with 1 and go to step 2. After termination c 1 ; c n are the components of p. Clearly, every grounded atom is a component by itself (since it has no variables) Helft [1] uses the notion of Horn clauses being linked, this notion is similar to sentences containing only one component. He states that non linked clauses are generally not meaningful . The following lemma states that disallowing more component sentences does not make a refinement operator defined on ....

N. Helft. Inductive Generalization: A Logical Framework. In I. Bratko and N. Lavrac, editor, Progress in Machine Learning: EWSL-87, pages 149--157. Sigma Press, Wilmslow, England, 1987.

....evolution of the logic language VL 21 [Michalski, 1980] Indeed, both examples and hypotheses are expressed as VL 21 generally Horn clauses [Grant Subrahmanian, 1995] Each example is represented by one ground linked range restricted definite clause. A definition of linked clause can be found in [Helft, 1987], while the definitions of range restrictedness and definite clause are in [DeRaedt, 1992] Each hypothesis is a set of VL 21 linked range restricted definite clauses with the same head. An example E is positive for a hypothesis H if its head has the same descriptor and sign as the head of the ....

Helft, N. (1987). Inductive Generalization: A Logical Framework. In I. Bratko & N. Lavrac (Eds.), Progress in Machine Learning - Proceedings of EWSL 87: 2nd European Working Session on Learning, 149-157, Sigma Press: Wilmslow.

.... is adopted as a generalization model, there exist no ideal refinement operators [45, 46] Research efforts in the area of ILP have been directed to improve the efficiency of the search by restricting full first order Horn clause logic bymeans of suitable language biases, such as linkedness [18], ij determinacy [29] Datalog (i.e. function free) clauses [31, 35] rule models [22] antecedent description grammars [5] clause sets [1] and literal templates [44] However, these language biases are not sufficient to solve the problemofdefining ideal refinement operators. Indeed,as Niblett ....

.... P(x i , x j ) 1 i, j n, i j , n 2 C = q : P(x 1 , x 1 ) Most systems that learn Horn clauses from examples adopt the language bias of linkedness in order to restrict the search space and to avoid generating quite insignificant clauses. A formal definition of linkedness can be found in [18, 38]. The uncovered infinite chains (E 3 n ) n 1 and (G n ) n 2 consist of clauses that are not linked, therefore it could be guessed that, if the learning system adopts such a language bias, it is possible to define ideal refinement operators. Unfortunately, even in the space of linked Datalog ....

Helft, N., Inductive Generalization: A Logical Framework, in Progress in Machine Learning - Proceedings of EWSL87:2ndEuropeanWorking Session onLearning, I. Bratko&N.Lavrac (Eds.), Sigma Press, Wilmslow,149157, 1987.

....x) and D = p(x; y; z) p(z; x; y) Then we have C , D, since D is a resolvent of C resolved with itself, and C is a resolvent of D resolved with itself. We also have C 6 D, and even C 6 D. It has been claimed that implication and subsumption are equivalent for function free clauses (Helft, 1987). This is wrong as shown by the example above. The above example also shows that if a clause C implies a clause D then C does not necessarily subsume D. It is well known that implication is a strictly weaker relation between clauses than subsumption. Proposition 3 Let C and D be two clauses. ....

Helft, N. (1987). Inductive generalization: A logical framework. In Proceedings of the Second European Working Session on Learning. Sigma Press, Wilmslow, England.

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N. Helft, Inductive generalization: a logical framework. in: Progress in Machine Learning, I. Bratko and N. Lavra c, eds, Sigma Press, 1987, 149--157.

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N. Helft. Inductive generalization: A logical framework. In Proceedings of the Second Working Session on Learning, pages 149-157, 1987.

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Helft N., 1987. Inductive Generalization: A Logical Framework, Progress in Machine Learning, proceedings of EWSL 87, I. Bratko, N. Lavrac (Eds.), Sigma Press, Bled, Yugoslavia, pp. 149-157.

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N. Helft. Inductive generalization: A logical framework. In Proceedings of the Second Working Session on Learning, pages 149--157, 1987.

No context found.

Helft, N.: Inductive Generalization: A Logical Framework. In: Bratko, I., Lavrac, N. #eds.#: Progress in Machine Learning - Proc. of the EWSL87, Sigma Press, London #1987# 149-157.

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Helft N., 1987. Inductive Generalization: A Logical Framework, Progress in Machine Learning, proceedings of EWSL 87, I. Bratko, N. Lavrac (Eds.), Sigma Press, Bled, Yugoslavia, pp. 149-157.

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Helft, N. (1987). Inductive generalization: a logical framework. In I. Bratko & N. Lavrac (Eds.), Progress in Machine Learning. (pp. 149-157).

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