Distances and limits on Herbrand interpretations

Nienhuys-Cheng, Shan-Hwei

doi:10.1007/bfb0027329

Cited by 22 publications

(12 citation statements)

References 6 publications

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“…Hence, the need for mechanisms to assess a degree of similarity among logic descriptions. Previous works on similarity/distance measures and techniques developed for comparing firstorder descriptions are concerned with flexible matching (Esposito, 1992), supervised learning (Bisson, 1992a;Emde, 1996;Domingos, 1995;Sebag, 1997;NienhuysCheng, 1998;Ramon, 2002;Kodratoff, 1986) and unsupervised learning (Thompson, 1989;Ramon, 1999;Bisson, 1992b;Blockeel, 1998). The similarity framework for FOL descriptions presented in the following overcomes some problems that are present in those works: it does not require assumptions and simplifying hypotheses (statistical independence, mutual exclusion) to ease the probability handling, no prior knowledge of the representation language is required and is not based on the presence of 'mandatory' relations, the user must not set weights on the predicates' importance, it can be easily extended to handle negative information, it avoids the propagation of similarity between subcomponents that poses the problem of indeterminacy in associations, it yields a unique value as a result of a comparison, which is more understandable and comfortable for handling, it is based directly on the structure, and not on derived features.…”

Section: Similarity Frameworkmentioning

confidence: 99%

FOL Learning for Knowledge Discovery in Documents

et al. 2012

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This chapter proposes the application of machine learning techniques, based on first-order logic as a representation language, to the real-world application domain of document processing. First, the tasks and problems involved in document processing are presented, along with the prototypical system DOMINUS and its architecture, whose components are aimed at facing these issues. Then, a closer look is provided for the learning component of the system, and the two sub-systems that are in charge of performing supervised and unsupervised learning as a support to the system performance. Finally, some experiments are reported that assess the quality of the learning performance. This is intended to prove to researchers and practitioners of the field that first-order logic learning can be a viable solution to tackle the domain complexity, and to solve problems such as incremental evolution of the document repository.

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Section: Similarity Frameworkmentioning

confidence: 99%

FOL Learning for Knowledge Discovery in Documents

et al. 2012

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“…[13] organizes terms in an importance-related hierarchy, and proposes a distance between terms based on interpretations and a level mapping function that maps every simple expression on a natural number. [15] presents a distance function between atoms based on the difference with their lgg, and uses it to compute distances between clauses.…”

Section: Related Workmentioning

confidence: 99%

Generalization-Based Similarity for Conceptual Clustering

Ferilli

Basile

Mauro

et al. 2008

Lecture Notes in Computer Science

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Abstract. The availability of techniques for comparing descriptions has many applications in Artificial Intelligence, ranging from description selection to flexible matching, from instance-based learning to clustering. Due to the complexity of handling First-Order Logic formulae, where the presence of relations causes various portions of one description to be possibly mapped in different ways onto another description, few works are available in the literature for this kind of representations. This paper tackles the case of Conceptual Clustering, where a new approach to similarity evaluation, based on both syntactic and semantic features, is exploited to support the task of grouping together similar items according to their relational description. After presenting a framework for Horn Clauses (including criteria, a function and composition techniques for similarity assessment), classical clustering algorithms are exploited to carry out the grouping task. Experimental results on real-world datasets prove the effectiveness of the proposal.

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“…k clauses are choosen and the truth values of whether each clause covers the example or not are used as k features for a distance on the space {0, 1} k between the examples. [6] organizes terms in an importance-related hierarchy, and proposes a distance between terms based on interpretations and a level mapping function that maps every simple expression on a natural number. [7] presents a distance function between atoms based on the difference with their lgg, and uses it to compute distances between clauses.…”

Section: Related Workmentioning

confidence: 99%

“…[7] presents a distance function between atoms based on the difference with their lgg, and uses it to compute distances between clauses. It consists of a pair: the first component extends the distance in [6] and is based on the differences between the functors on both terms, while the second component is based on the differences in occurrences of variables and allows to differentiate cases where the first component cannot. …”

Section: Related Workmentioning

confidence: 99%

Similarity-Guided Clause Generalization

Ferilli

Basile

Mauro

et al. 2007

Lecture Notes in Computer Science

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Abstract. Few works are available in the literature to define similarity criteria between First-Order Logic formulae, where the presence of relations causes various portions of one description to be possibly mapped in different ways onto another description, which poses serious computational problems. Hence, the need for a set of general criteria that are able to support the comparison between formulae. This could have many applications; this paper tackles the case of two descriptions (e.g., a definition and an observation) to be generalized, where the similarity criteria could help in focussing on the subparts of the descriptions that are more similar and hence more likely to correspond to each other, based only on their syntactic structure. Experiments on real-world datasets prove the effectiveness of the proposal, and the efficiency of the corresponding implementation in a generalization procedure.

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Distances and limits on Herbrand interpretations

Cited by 22 publications

References 6 publications

FOL Learning for Knowledge Discovery in Documents

FOL Learning for Knowledge Discovery in Documents

Generalization-Based Similarity for Conceptual Clustering

Similarity-Guided Clause Generalization

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