A Theory of Finite Closure Spaces Based on Implications

Wild, Marcel

doi:10.1006/aima.1994.1069

Cited by 57 publications

(72 citation statements)

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“…It turns out that this canonical form is, in essence, the Guigues-Duquenne basis (the GD basis) which was introduced in Guigues and Duquenne (1986). Here, we introduce it in a form that is, to our knowledge, novel, although it is relatively close to the approaches of Maier (1980), Wild (1994). Our construction is based on the notion of saturation, a notion that has been used already in the context of propositional Horn functions (Arias and Balcázar 2008;Arias et al 2006), as well as in the context of Inductive Logic Programming (Rouveirol 1994).…”

Section: The Guigues-duquenne Basis For Definite Hornmentioning

confidence: 99%

“…The following Lemma is a variant of a result of Wild (1994) translated into our notation. We include the proof which is, in fact, missing from Wild (1994).…”

Section: Is Left-saturated If and Only If The Following Implication Imentioning

confidence: 99%

“…Some of the technical lemmas and theorems in this paper are based on previous concepts and results of Wild (1994), Guigues and Duquenne (1986), Maier (1980); we credit this fact appropriately throughout this presentation. As a general overview, we have adopted the following: the "bullet" operator (…”

Section: Introductionmentioning

confidence: 99%

“…To the best of our knowledge, the earliest description is due to Maier (1980) who in 1980 studied minimality of covers of sets of functional dependencies in the field of Theory of Databases. Later on in 1986, in the field of Formal Concept Analysis, the Guigues-Duquenne basis or GD basis (Guigues and Duquenne 1986;Wild 1994) was described. Finally, very recently, Bertet and Monjardet (2010) explores the history of this and other aspects that we study in the paper.…”

Section: Introductionmentioning

confidence: 99%

“…3.1 is directly taken from Wild (1994), the "star" operator ( ) is standard in the field of study of Closure Spaces, and the GD basis comes from the Formal Concept Analysis literature. Most of the results in Sect.…”

Section: Introductionmentioning

confidence: 99%

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Construction and learnability of canonical Horn formulas

Arias

Balcázar

2011

Mach Learn

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We describe an alternative construction of an existing canonical representation for definite Horn theories, the Guigues-Duquenne basis (or GD basis), which minimizes a natural notion of implicational size. We extend the canonical representation to general Horn, by providing a reduction from definite to general Horn CNF. Using these tools, we provide a new, simpler validation of the classic Horn query learning algorithm of Angluin, Frazier, and Pitt, and we prove that this algorithm always outputs the GD basis regardless of the counterexamples it receives.

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Section: The Guigues-duquenne Basis For Definite Hornmentioning

confidence: 99%

“…The following Lemma is a variant of a result of Wild (1994) translated into our notation. We include the proof which is, in fact, missing from Wild (1994).…”

Section: Is Left-saturated If and Only If The Following Implication Imentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Construction and learnability of canonical Horn formulas

Arias

Balcázar

2011

Mach Learn

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Color separation for improved perceived image quality in terms of graininess and gamut

Elias

Nyström

Gooran

2016

Color Research & Application

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Multi‐channel printing employs additional inks to improve the perceived image quality by reducing the graininess and augmenting the printer gamut. It also requires a color separation that deals with the one‐to‐many mapping problem imposed when using more than three inks. The proposed separation model incorporates a multilevel halftoning algorithm, reducing the complexity of the print characterization by grouping inks of similar hues in the same channel. In addition, a cost function is proposed that weights selected factors influencing the print and perceived image quality, namely color accuracy, graininess and ink consumption. The graininess perception is qualitatively assessed using S‐CIELAB, a spatial low‐pass filtering mimicking the human visual system. By applying it to a large set of samples, a generalized prediction quantifying the perceived graininess is carried out and incorporated as a criterion in the color separation. The results of the proposed model are compared with the separation giving the best colorimetric match, showing improvements in the perceived image quality in terms of graininess at a small cost of color accuracy and ink consumption. © 2016 Wiley Periodicals, Inc. Col Res Appl, 42, 486–497, 2017

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Characterizing Implications of Injective Partial Orders

Balcázar

Garriga

Conceptual Structures: Knowledge Architectures for Smart Applications

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It is known that implications in powerset-based closure systems correspond to Horn approximations in propositional logic frameworks. Here we focus on the problem of implications between injective partial orders. We set up the definitions that allow one to apply standard constructions of implications, and formally characterize the propositional theory obtained. We describe also some experimental applications of our development.

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A Theory of Finite Closure Spaces Based on Implications

Cited by 57 publications

References 0 publications

Construction and learnability of canonical Horn formulas

Construction and learnability of canonical Horn formulas

Color separation for improved perceived image quality in terms of graininess and gamut

Characterizing Implications of Injective Partial Orders

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