Lattices, closures systems and implication bases: A survey of structural aspects and algorithms

Bertet, Karell; Demko, Christophe; Viaud, Jean-François; Guerin, Clément

doi:10.1016/j.tcs.2016.11.021

Cited by 34 publications

(26 citation statements)

References 20 publications

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“…An implicational base (X, Σ) is a set Σ of implications of the form A B where A ⊆ X and B ⊆ X; see [Wil17,BDVG18]. In this paper we only consider implicational bases in their equivalent unit form where |B| = 1 for every implication, and denote by A b such implications, where B = {b}.…”

Section: Preliminariesmentioning

confidence: 99%

Dualization in Lattices Given by Implicational Bases

Defrain

Nourine

2019

Formal Concept Analysis

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It was recently proved that the dualization in lattices given by implicational bases is impossible in output-polynomial time unless P=NP. In this paper, we show that this result holds even when the premises in the implicational base are of size at most two. Then we show using hypergraph dualization that the problem can be solved in output quasi-polynomial time whenever the implicational base has bounded independent-width, defined as the size of a maximum set of implications having independent conclusions. Lattices that share this property include distributive lattices coded by the ideals of an interval order, when both the independent-width and the size of the premises equal one.

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Section: Preliminariesmentioning

confidence: 99%

Dualization in Lattices Given by Implicational Bases

Defrain

Nourine

2019

Formal Concept Analysis

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“…Implications An implication, denoted by A =⇒ B, is a pair of attribute sets (A, B), A, B ⊆ M where all the objects that own the attributes of A (premise) also own the ones of B (conclusion): A ⊆ B . For example, the implication (I1) indicates that no plant of genus1 is used in medical care: There are several types of implication sets and bases [1] that can be computed from a FC. Binary implications such as (I1) can also be obtained from C and the introducing attributes' concepts, e.g.…”

Section: Rca Takes a Relational Context Family (Rcf) As Inputmentioning

confidence: 99%

“…Life sciences data raise other issues, such as indeterminate species [9]. Association and Implication extraction is closely connected to FCA [1,11]. Implications with premises restricted to one attribute, have been extracted from the result of RCA combined with AOC-posets [2].…”

Section: Related Workmentioning

confidence: 99%

Combining Implications and Conceptual Analysis to Learn from a Pesticidal Plant Knowledge Base

Mahrach

Gutierrez

Huchard

et al. 2021

Lecture Notes in Computer Science

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Supporting organic farming aims to find alternative solutions to synthetic pesticides and antibiotics, using local plants, to protect crops. Moreover, in the One Health approach (OHA), a pesticidal plant should not be harmful to humans, meaning it cannot be toxic if the crop is consumed or should have a limited and conscious use if it is used for medical care. Knowledge on plant use presented in the scientific literature was compiled in a knowledge base (KB). The challenge is to develop a KB exploration method that informs experts (including farmers) about protection systems properties that respect OHA. In this paper, we present a method that extracts the Duquenne-Guigues basis of implications from knowledge structured using Relational Concept Analysis (RCA). We evaluate the impact of three data representations on the implications and their readability. The experimentation is conducted on 562 plant species used to protect 15 crops against 29 pest species of the Noctuidae family. Results show that consistently splitting data into several tables fosters less redundant and more focused implications.

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“…This choice is motivated by the fact that implicative systems can be defined on the feature set only. Moreover, several algorithms enable to switch from a representation to another (formal context, concept lattice, implicative system basis) in a canonical way, as they are based on bijections between these objects through a closure operator [54].…”

Section: Addressing Scaling Issuesmentioning

confidence: 99%

FCA for software product line representation: Mixing configuration and feature relationships in a unique canonical representation

Carbonnel¹,

Bertet

Huchard³

et al. 2020

Discrete Applied Mathematics

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Software Product Line Engineering (SPLE) is a set of methods to help build a collection of software systems which are similar enough to enable appropriate artefact reuse. An important task consists in documenting in variability models the common and variable features which may compose the similar software systems along with compatibility constraints between these features. Several models and formalisms have been proposed to model variability: each one of them has specific properties making it pertinent to support certain management operations, which are of primary importance in SPLE. Switching from one kind of variability model to another is thus important to benefit from a wide range of operations and efficiently manage a software product line. In this paper, we review the various approaches proposed to manage and organise features and product configurations (a product configuration being a chosen subset of features). We discuss the originality of concept lattices, canonical structures presenting a dual view on features and configurations, and the advantages to use these structures as variability representations. Switching from existing variability models to an equivalent concept lattice raises scaling issues related to the size of the needed input dataset and thus hinders their exploitation. We propose an alternative relying on implicative systems and define a transformation method which does not suffer from scaling issues.

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Lattices, closures systems and implication bases: A survey of structural aspects and algorithms

Cited by 34 publications

References 20 publications

Dualization in Lattices Given by Implicational Bases

Dualization in Lattices Given by Implicational Bases

Combining Implications and Conceptual Analysis to Learn from a Pesticidal Plant Knowledge Base

FCA for software product line representation: Mixing configuration and feature relationships in a unique canonical representation

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