48,977 research outputs found

    Least Generalizations and Greatest Specializations of Sets of Clauses

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    The main operations in Inductive Logic Programming (ILP) are generalization and specialization, which only make sense in a generality order. In ILP, the three most important generality orders are subsumption, implication and implication relative to background knowledge. The two languages used most often are languages of clauses and languages of only Horn clauses. This gives a total of six different ordered languages. In this paper, we give a systematic treatment of the existence or non-existence of least generalizations and greatest specializations of finite sets of clauses in each of these six ordered sets. We survey results already obtained by others and also contribute some answers of our own. Our main new results are, firstly, the existence of a computable least generalization under implication of every finite set of clauses containing at least one non-tautologous function-free clause (among other, not necessarily function-free clauses). Secondly, we show that such a least generalization need not exist under relative implication, not even if both the set that is to be generalized and the background knowledge are function-free. Thirdly, we give a complete discussion of existence and non-existence of greatest specializations in each of the six ordered languages.Comment: See http://www.jair.org/ for any accompanying file

    E-Generalization Using Grammars

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    We extend the notion of anti-unification to cover equational theories and present a method based on regular tree grammars to compute a finite representation of E-generalization sets. We present a framework to combine Inductive Logic Programming and E-generalization that includes an extension of Plotkin's lgg theorem to the equational case. We demonstrate the potential power of E-generalization by three example applications: computation of suggestions for auxiliary lemmas in equational inductive proofs, computation of construction laws for given term sequences, and learning of screen editor command sequences.Comment: 49 pages, 16 figures, author address given in header is meanwhile outdated, full version of an article in the "Artificial Intelligence Journal", appeared as technical report in 2003. An open-source C implementation and some examples are found at the Ancillary file

    A critical view on invexity

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    The aim of this note is to emphasize the fact that in many papers on invexity published in prestigious journals there are not clear definitions, trivial or not clear statements and wrong proofs. We also point out the unprofessional way of answering readers' questions by some authors. We think that this is caused mainly by the lack of criticism of the invexity communityComment: The paper was submitted to JOTA in December 2007 and practically accepted by the AE handling it in March 2008. Being a critical paper, the EiC asked the authors of the criticised articles to say their opinion. With the change of the EiC's, apparently the paper was not transmitted to the new Ei

    Median problems in networks

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    The P-median problem is a classical location model “par excellence”. In this paper we, first examine the early origins of the problem, formulated independently by Louis Hakimi and Charles ReVelle, two of the fathers of the burgeoning multidisciplinary field of research known today as Facility Location Theory and Modelling. We then examine some of the traditional heuristic and exact methods developed to solve the problem. In the third section we analyze the impact of the model in the field. We end the paper by proposing new lines of research related to such a classical problem.P-median, location modelling
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