Lina Mahrach
email: lina.mahrachlm@gmail.com

Alain Gutierrez

Marianne Huchard

Priscilla Keip

Pascal Marnotte

Pierre Silvie

Pierre Martin

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

Keywords: Relational Concept Analysis, Duquenne-Guigues basis, Implication Rules, Life Sciences Knowledge Base, One Health, Formal Concept Analysis

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.

Introduction

Reducing the use of synthetic pesticides and antibiotics is a major challenge for the environment and living organisms. Moreover, for the Global South countries, it is also crucial to preserve biodiversity and design sustainable production systems (SPS) that respect the One Health approach (OHA) [START_REF] Frank | One world, one health, one medicine[END_REF]. OHA calls for an interdisciplinary and intersectoral action in the public management of health problems at the interface between humans, animals, and their shared environment. An alternative solution to synthetic pesticides and antibiotics accepted by OHA is the use of local plants, in the form of essential oil or aqueous solution, with a pesticidal or anti-parasitic effect. Using such plants requires ensuring that they are not harmful to humans. Some plants can indeed be toxic to humans when inhaled during their spray in the field or ingested through crop consumption. Other plants, also used by humans for medical care, can induce a resistance to certain molecules through excessive absorption. One challenge for the scientific experts and for the farmers is to understand the properties and constraints of the already known protection systems, composed of a crop to be protected against a pest using a protecting plant, with respect to OHA.

A significant number of protection systems have been extracted in the scientific literature and gathered in the Knomana knowledge base [START_REF] Martin | Knomana -usage des plantes à effet pesticide, antimicrobien, antiparasitaire et antibiotique[END_REF]. Knomana includes several datasets. Among them, PPAf (Pesticide Effect Plant of Africa) currently gathers 44270 descriptions of plants used for plant, animal, human, and public health. In PPAf, each use is described using 70 data, such as the protected organism (e.g. crop, fish, human being), the target organism (e.g insect, fungus, bacterium), the location, and the usage domain (plant, animal, environmental, human, or public health). Knomana also includes PAL (Edible plants), which informs whether plants are consumed by humans as food or drink.

In this paper, we make the assumption that implications are a relevant formalism for delivering information on protection systems relative to OHA. We choose to build the Duquenne-Guigues basis (DGB) of implications for its quality of being a non redundant implication set of minimal cardinality. Besides, we assess the impact of three data representations on the implication form and readability. These three representations reconcile the two datasets and split them into one or several data tables. When the representation has several data tables, we build the DGB of implications from the extended formal contexts computed by Relational Concept Analysis (RCA) [START_REF] Hacene | Relational concept analysis: mining concept lattices from multi-relational data[END_REF] with AOC-posets. An experimentation is conducted on a Knomana excerpt composed of 562 plants species used to protect 15 crops against 29 pest species of the Noctuidae family. Results show that consistently reconciling datasets and splitting the data into several tables fosters less redundant and more focused implications.

Section 2 introduces the background and outlines the approach. Section 3 describes the Knomana excerpt and the three studied representations. Section 4 reports and discusses the experiment. Section 5 exposes related research and Section 6 concludes and draws future work.

Approach

This section introduces the approach, which combines RCA and the computation of the DGB of implications.

RCA. RCA is designed to analyze a dataset conforming to the entity-relationship model [START_REF] Hacene | Relational concept analysis: mining concept lattices from multi-relational data[END_REF]. RCA is an extension of Formal Concept Analysis (FCA) [START_REF] Ganter | Formal Concept Analysis -Mathematical Foundations[END_REF]. FCA seeks to extract formal concepts from a formal context (FC) K = (G, M, I) where G is an object set, M is an attribute set and I ⊆ G × M . Two operators, both denoted by , associate object sets with attribute sets. For O ⊆ G, the set of attributes shared by the objects of O is O = {m|∀g ∈ O, (g, m) ∈ I}. For A ⊆ M , the set of objects that share the attributes of A is A = {g|∀m ∈ A, (g, m) ∈ I}. A formal concept C = (E xtent(C), I ntent(C)) associates a maximal object group (extent) with their maximal shared attribute group (intent): E xtent(C) = I ntent(C) . More generally, we denote by C the concept order:

C 1 C C 2 when I ntent(C 2 ) ⊆ I ntent(C 1 ) and E xtent(C 1 ) ⊆ E xtent(C 2 ).
The set of all concepts, provided with C , forms the concept lattice. The lowest (w.r.t. C ) concept owning one object is its introducer concept. The highest (w.r.t. C ) concept owning one attribute is its introducer concept. The suborder of the concept lattice restricted to these introducer concepts is called the AOC-poset (Attribute-Object Concept poset). For instance, in Table 1, the FC OrganismInfo describes plant (pl i ), crop (prot i ), and pest (pest i ) organisms using their genus (genus i ) and their non-use in medical care (no-medical). Plants pl1 and pl2 are grouped as a concept being both from genus1 and not used in medical care. pl1 and pl2 can as well be grouped with prot1 and prot2 as they are not used in medical care. As presented in Fig. 1

RCA takes a

Relational Context Family (RCF) as input. A RCF is a pair (K, R) where K is a set of FCs (K = {K i = (G i , M i , I i )} i=1,2,...,n ), and each FC describes an object category. R is a set of relational contexts (RC) between the objects of the FCs. R = {r j } j=1,2,...,p and r j ⊆ G k × G l for k, l ∈ {1, 2, . . . , n}. To compute the concepts for each FC considering the RCs, RCA builds relational attributes qr(C), where q is a quantifier (e.g. the existential quantifier ∃ or the universal quantifier ∀), r is a RC, and C is a concept on the objects of the co-domain of r. These attributes thus group the individual-to-individual relationships into individual-to-concept relationships. To compute the final conceptual structure family, RCA alternates between building conceptual structures associated with FCs (such as a concept lattice or an AOC-poset) and extending the FCs with relational attributes, including the concepts of these structures, until a fix-point is reached. Table 1 presents a RCF, composed of the FCs Or-ganismInfo and ProtSystem and 3 RCs, i.e. uses, protects, and treats. These 3 RCs respectively indicate the plant, the crop, and the pest for each protection system. In this example, the FC ProtSystem is finally extended with relational attributes formed with the quantifier ∃, a RC (i.e. uses, protects, or treats) and a concept of OrganismInfo as shown in Table 2. In Fig. 1, the concepts built on the extended FC (EFC) ProtSystem group and organize protection systems by considering the relational attributes. 1, with the protection system lattice to the left and an organism one to the right. A plain or dashed arrow represents respectively a subconcept-superconcept relation or a crosslattice link materialized by a relational attribute. Concept C SystP rot 31 groups 6 protection systems (1, 3, 4, 5, 6, 7) using a plant from concept C Org 22, i.e. pl1, pl2, or pl4, not used in medical care. C SystP rot 25, which is a subconcept of C SystP rot 31, groups 4 protection systems [START_REF] Fayyad | The KDD process for extracting useful knowledge from volumes of data[END_REF][START_REF] Frank | One world, one health, one medicine[END_REF][START_REF] Ganter | Formal Concept Analysis -Mathematical Foundations[END_REF][START_REF] Guigues | Famille minimale d'implications informatives résultant d'un tableau de données binaires[END_REF], informing that they use a plant from genus1 (∃uses(C Org 15)), not used in medical care (∃uses(C Org 22)) to protect a crop from genus6 (∃protects(C Org 13)) against a pest of genus4 (∃treats(C Org 18)).

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 [START_REF] Bertet | Lattices, closures systems and implication bases: A survey of structural aspects and algorithms[END_REF] 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. in Fig. 1: C Org 15 introduces genus1, while its superconcept C Org 22 introduces no-medical. The Duquenne-Guigues Basis (DGB) of implications can be defined upon pseudo-intents [START_REF] Guigues | Famille minimale d'implications informatives résultant d'un tableau de données binaires[END_REF]. A pseudointent is an attribute set P i ⊆ M such that: P i is not an intent (P i = P i ); for any other pseudo-intent P j ⊂ P i , P j ⊂ P i . The DGB is the implication set

{genus1} =⇒ {no -medical} (I1)
{P i =⇒ P i |P i is a pseudo-intent}.
It is canonical and a cardinality minimal set of non redundant implications, from which all implications can be produced.

Our approach. In our work, we compute the DGB of implications, that is usually built for an FC. When using RCA, implications are extracted when the fix-point is reached. For a FC which is not extended, because it is not the object set of a RC, the DGB of implications is directly computed on itself. For a FC which is extended, the DGB is built from its extension (EFC). In our approach, AOC-posets are built at each RCA step. For an easier interpretation of the implications extracted from the EFCs, the concepts in the relational attributes are recursively replaced by the 'non-relational' attributes that serve as seeds for these concepts [START_REF] Wajnberg | Analyse relationnelle de concepts : une méthode polyvalente pour l'extraction de connaissance[END_REF][START_REF] Wajnberg | Concept analysis-based association mining from linked data: A case in industrial decision making[END_REF]. For instance, the implication (I2) becomes (rewritten I2): 4) and ( 5)

{∃treats(C Org 18)} =⇒ {∃uses(C Org 22)} (I2) {∃treats(genus4)} =⇒ {∃uses(no -medical)} (rewritten I2) Both (
The DGBs of implications are built for FC OrganismInfo and EFC ProtSystem.

Three Representations of the Datasets

This section presents the datasets and their combination through three representations splitting the data differently. Our objective is to assess the impact of the splitting on the form and the readability of the implications.

The datasets. The datasets concern 29 pest species belonging to 15 genera of the Noctuidae family [START_REF] Martin | Dataset on noctuidae species used to evaluate the separate concerns in conceptual analysis: Application to a life sciences knowledge base[END_REF]. To control these species on 15 crops (e.g. tomato, maize, cotton) belonging to seven families, 562 plant species, belonging to 352 genus and to 94 families, are identified. The first dataset, which is an excerpt of PPAf, contains 721 protection systems, i.e. triplets (plant, pest, crop) describing the use of a plant to protect a crop against a Noctuidae pest at the species taxonomic level. The modeling interest of the Noctuidae family raises on the polyphagous or highly polyphagous nature of some of its pest species' diet. A polyphagous pest, such as Trichilia pallida, attacks crops from various genera of the same family, while a highly polyphagous pest, such as Spodoptera frugiperda, attacks crops from various families. In this first dataset, some publications do not specify the crop but the plant and the pest, mainly because of the polyphagous nature of the pest diet. To obtain a triplet in this case, a generic name was provided to the crop. Five generic species names were adopted, namely CropBrasS, CropFabaS, CropMalvS, CropPoacS, and CropS. The first four correspond to a crop attacked by a polyphagous pest, respectively from Brassicaceae, Fabaceae, Malvaceae, and Poaceae family. CropS corresponds to a crop attacked by a highly polyphagous pest. To the best of our knowledge, and to be as cautious as possible, we consider that they are all consumed by humans, and that only CropMalvS and CropS are used for medical care. Finally, in this PPAf excerpt, six organism species (e.g. pepper, chickpea, and castor bean) are both described as a crop and a protecting plant.

The second dataset is another excerpt of PPAf and informs on the plants used for medical care. This information was extracted for each protecting plant and each crop listed in the first dataset. None of the pests is used for human and public health.

The last dataset, an excerpt of PAL, informs on the consumption of plants and crops by humans. This excerpt includes only plants and crops present in the first dataset. In this work, we consider that none of the pests are consumed by human or used in medical care.

The three representations. Combining the three datasets enables to representing SPSs that respect OHA. Three representations, leading to three different RCFs, were developed according to the reification of different entities and roles.

The Relational representation (Fig. 3a) considers five different entities. The three first represent the biological organisms. The first entity is crop. It is described using three attributes, i.e. crSpecies, crGenus, and crF amily, which respectively correspond to its species, its genus, and its family. The second entity is P est, i.e. an aggressor of a crop. It contains three attributes, i.e. peSpecies, peGenus, and peF amily, which respectively correspond to its species, its genus, and its family. The third entity is P lant. Plants are described using three attributes, i.e. plSpecies, plGenus, and plF amily, which respectively correspond to its species, its genus, and its family. The fourth entity represents the protection systems (P rotSystem). P rotSystem reifies the ternary relation linking plSpecies, crSpecies, and peSpecies. The last entity is OrganismInf o in which each organism is described using its name at the species, genus, and family taxonomic levels using respectively the attributes species, genus, and f amily. In addition OrganismInf o indicates whether the organism is consumed (attribute f ood) and whether it is used for medical care (attribute medical). P rotSystem includes the data from PPAf knowledge set, and OrganismInf o compiles the two other knowledge sets. The RCF for this representation is thus composed of five FCs (P rotSystem, P lant, Crop, P est, OrganismInf o). Boolean attributes are obtained through a nominal scaling of the attributes [START_REF] Ganter | Formal Concept Analysis -Mathematical Foundations[END_REF]. The RCF also contains six RCs: uses, protects, treats, pl CharactBy, cr CharactBy, and pe CharactBy.

The T woT ables representation (Fig. 3b) comports two entities. P rotSystem and OrganismInf o respectively represent the protection systems and the organisms, as in the Relational representation. This representation does not reify the role of the organisms in the protection systems, as does the Relational representation. The RCF for this representation is thus composed of two FCs (i.e. P rotSystem, OrganismInf o). The native (Boolean) attributes are obtained through a nominal scaling of the attributes. The RCF also contains three RCs: uses, protects, and treats.

The OneT able representation (Fig. 3c) reifies protection systems in an entity named CombinedSystem. This entity includes the attributes of entities P lant, Crop, and P est of the Relational representation. It also contains the medical and food attributes related to the protecting plant and to the crop, respectively named medicalP lant, f oodP lant, medicalCrop, and f oodCrop. Additional attributes were included to express relationships between data not formalized by this representation. plSpIsCrEw and plGeIsCrEw indicate respec- tively that a protecting species is a crop species in another triplet, and a protecting genus is a crop genus in another triplet. The attributes crSpIsP lEw and crGeIsP lEw indicate respectively that a crop species is a protecting species in another triplet, and a crop genus is a protecting genus in another triplet. multiU seP lSp, multiU seP lGe, and multiU seP lF a indicate whether the protecting plant, respectively at the species, genus, and family taxonomic levels, is both consumed and used for medical care. The RCF is here reduced to a single FC CombinedSystem, with attributes obtained by a nominal scaling of the CombinedSystem entity attributes.

Table 3 presents the size of the different representations, in terms of number of objects and attributes, number of relational attributes, and size of the AOCposets at the initial and at the last steps of RCA process.

Evaluation

This section presents (Sect. 4.1) and discusses (Sect. 4.2) the results obtained for the three data structures. The experiments were conducted using Cogui software platform 4 , which includes Java implementations of RCA and LinCbO [START_REF] Janostik | Pruning techniques in LinCbO for computation of the Duquenne-Guigues basis[END_REF]. Running times for the Java LinCbO implementation remain below 3229 ms for the most complex case (relational data model), summing the running times for all the EFCs.

Analysis of the implications obtained for the 3 representations

In this section, we analyze the DGB of implications for the three representations (cf. Table 4). For each one, we present a quantitative and a qualitative analysis describing the main implication patterns, and provide selected examples. To consider implications applicable to OHA, we focus on the ones with scope > 0.

Implications in Relational representation

OrganismInfo. The DGB contains 1168 implications: 1007 are held by one object (S = 1) and thus are very specific. Four types of implications are observed. The first one informs about the uses in medical care and food care for a species, a genus, or a family, e.g. the Meliaceae are not consumed (with S = 35) 5 :

F amily M eliaceae =⇒ F ood
The second type gives more specific information about subsets of species in families and genus, e.g. the species of Annonaceae, which are not consumed, are also not used in medical care. The third type reflects taxonomy: a genus implies a family or a species implies a genus, e.g. Genus Salvia implies Family Lamiaceae (with S = 18):

Genus Salvia =⇒ F amily Lamiaceae

The fourth implication type reveals data variety in the dataset. For instance species of Lythraceae family are not consumed and not used for care, and are exclusively from Genus Lythrum.

Crop The next example of implication (with S = 1), indicates that Malvaceae crops, not used in medical care, are restricted to Gossypium Genus and not consumed:

CrF amily M alvaceae, ∃cr CharactBy(M edical ), ∃cr CharactBy(F amily M alvaceae) =⇒ CrSpecies GossypiumHirsutum, CrGenus Gossypium, ∃cr CharactBy(F ood ), ∃cr CharactBy(Species GossypiumHirsutum&Genus Gossypium)

Pest. The DGB contains 80 implications. Some implications reflect the taxonomy, already highlighted in OrganismInf o, and add no information for the experts. The Smax implication (Smax = 29) indicates that all pests are from the Noctuidae family, not consumed, and not used in medical care.

Plant. The DGB contains 1815 implications. Most of the implications (1509) hold for a single plant. As for crops and pests, the implications either reflect taxonomy or information about human consumption and medical care usage (restricted to organisms that play the role of protecting plant). Some other implications are true for protecting plants only, such as the following one, indicating that family Poaceae plants not used in medical care, are also not consumed (with S = 2):

P lF amily P oaceae, ∃pl CharactBy(M edical ), ∃pl CharactBy(F amily P oaceae) =⇒ ∃pl CharactBy(F ood )

ProtectionSystem. The DGB contains 1391 implications, among which 566 held by more than one object. This result informs the expert on the numerous combinations of information existing in the datasets. The implication with Smax = 721, i.e. held by all objects, indicates that all systems treat Noctuidae. Within the 1391 implications, many implications types are present. They gather knowledge on the various roles of the organisms. We present some representative examples with diverse S values. The following implication (with S = 380), named Rel2, informs that when the studied protection systems treat Spodoptera Genus (Noctuidae Family), with a plant not consumed and not used in care, then the crop is used in medical care:

∃treats(P eF amily N octuidae), ∃treats(P eGenus Spodoptera), ∃uses(pl CharactBy(F ood )), ∃uses(pl CharactBy(M edical )) =⇒ ∃protects(cr CharactBy(M edical X)) (Rel2)

The next implication (with S = 8) indicates that when studied protection systems treat Noctuidae Family with Genus Cymbopogon plants, then this is with Poaceae plants on consumed crops and the plants are used in medical care. Poaceae are also crops, and thus subject to implications for both roles:

∃treats(P eF amily N octuidae), ∃uses(P lGenus Cymbopogon) =⇒ ∃uses(P lF amily P oaceae), ∃protects(cr CharactBy(F ood X)), ∃uses(pl CharactBy(M edical X))

The next implication (with S = 4) indicates that when the protection systems protect Poaceae crops consumed and not used in medical care, to treat Noctuidae pests, using non consumed plants, then this is with Meliaceae plants used in medical care:

∃protects(CrF amily P oaceae), ∃treats(P eF amily N octuidae), ∃uses(pl CharactBy(F ood )) ∃protects(cr CharactBy(F ood X)), ∃protects(cr CharactBy(M edical )), =⇒ ∃uses(P lF amily M eliaceae), ∃uses(pl CharactBy(M edical X))

Implications in T woT ables representation As the FC OrganismInf o is similar to the one of Relational, it thus provides the same implication set. The DGB contains 1395 implications for the FC P rotSystem. This implication number is very similar to the one of the P rotSystem Relational representation. As an illustration, two implications are compared. The first one, TT1, focuses on the crop role:

∃protects(F ood ), ∃protects(M edical X), ∃treats(F amily N octuidae) ∃treats(F ood ), ∃treats(M edical ) =⇒ ∃protects(F amily Euphorbiaceae), ∃protects(Species RicinusCommunis&Genus Ricinus), ∃treats(Genus Spodoptera), ∃treats(Species SpodopteraLitura), ∃uses(F ood ), ∃uses(M edical ), ∃uses(F amily Asteraceae), ∃uses(Species W ollastoniaDentata&Genus W ollastonia) (TT1)

It is one of the 5 implications that mention Ricinus Communis. Compared to its Relational representation formulation, i.e. Rel1, it mixes information proper to Ricinus Communis as a crop with additional information on the protection systems, in particular the usage of Wollastonia Dentata as the protecting plant. In this case, implications of the Relational representation are easier to read, as they focus on organism roles. The second implication, TT2, is held by Noctuidae that are not consumed and not used in medical care:

∃treats(F ood ), ∃treats(M edical ), ∃treats(F amily N octuidae), ∃treats(Genus Spodoptera), ∃uses(F ood ), uses(M edical

) =⇒ ∃protects(M edical X) (TT2)
This information is not provided in its corresponding Relational representation formulation Rel2 because it is not needed: in Relational representation it in-deed appears in a separate and more precise way through the P est implication indicating that Noctuidae are never consumed, nor used in medical care. Rel2 is more focused and more synthetic. The role has been encoded in the attribute name (e.g. M edicalCrop), rather than in the relations. Compared to Rel1, attributes about the protection system are included, e.g. P eGenus Spodoptera. Compared to both Rel1 and TT1, additional attributes indicate multi-use purpose, e.g. that the crop Ricinus Communis is used elsewhere as a protecting plant (CrSpIsP lEw X), and the protecting plant Wollastonia Dentata is not used as a crop (P lSpIsCrEw ). Another example is OT2, where roles appear as attributes rather than through relations:

Implications in

P eGenus Spodoptera, P eF amily N octuidae, F oodP lant , M edicalP lant , M ultiU seP lSp , M ultiU seP lGe , M ultiU seP lF a =⇒ M edicalCrop X (OT2)

Information on food and medical care has not been encoded for pests in OneT able representation to simplify, being identical for all Noctuidae. Compared to both Rel2 and TT2, additional attributes complete the premise to indicate that the plant has no multiple uses, e.g. M ultiU seP lGe .

Discussion

Lessons Learned. There is many taxonomic information in the implications, and some are duplicated in several tables. Although this duplication helps reading separately the implications (not considering several FCs at the same time), it complicates the reading of implications. Some other taxonomic information, such as indicating species, genus, and family may seem redundant too, as the latter two can be deduced from the species. Nevertheless, it may be useful for the readers who are not totally familiar with the taxonomy. In addition, some implications only precise the taxonomy, such as species implies genus. These implications could be automatically discarded, as they correspond to initial data encoding. Different settings of the implication formulation could be proposed to the user depending on the expected information. Construct validity can be appreciated through the metrics and the qualitative analysis adopted to evaluate the effect of representation splitting. The metrics have been chosen in order to evaluate the feasibility in terms of structure size and implication number. The running time obtained thanks to LinCbO is very low. The obtained implications have been exhaustively examined, a task made easier by the substitution of the concept number by the seed attributes. Some recurring schemes and representative implications have been reported in the paper as a result of this analysis. Conclusion validity is concerned with the possibility of generalizing the observations. Knomana knowledge set has its own particularities, such as being organized around a ternary relation P lant × P est × Crop (protection system). Other secondary relations gravitate around this central relation. This has the effect of centralizing, for protection systems, the information coming from the other contexts. The implications reflect this organization. Using another dataset, not organized this way, conclusions may be different.

Effect of Splitting the representations. As shown in

Related Work

Modeling complex data with the objective of extracting knowledge is part of the Knowledge Discovery and Data Mining processes (KDD) [START_REF] Fayyad | The KDD process for extracting useful knowledge from volumes of data[END_REF]. This issue is addressed in FCA through various encoding schemes and extensions, starting with conceptual scaling [START_REF] Ganter | Formal Concept Analysis -Mathematical Foundations[END_REF]. In the case of RCA, data modeling includes choosing a kind of entity-relationship model with binary relationships and Boolean attributes. This requires deciding how data are separated in formal and relational contexts, and how to represent n-ary relations, e.g. ternary relations, a topic we studied in [START_REF] Keip | Effects of Input Data Formalisation in RCA for a Data Model with a Ternary Relation[END_REF]. Life sciences data raise other issues, such as indeterminate species [START_REF] Keip | Practical comparison of FCA extensions to model indeterminate value of ternary data[END_REF].

Association and Implication extraction is closely connected to FCA [START_REF] Bertet | Lattices, closures systems and implication bases: A survey of structural aspects and algorithms[END_REF][START_REF] Kuznetsov | Knowledge representation and processing with formal concept analysis[END_REF]. Implications with premises restricted to one attribute, have been extracted from the result of RCA combined with AOC-posets [START_REF] Dolques | Performance-friendly rule extraction in large water data-sets with AOC posets and relational concept analysis[END_REF]. More recently, M. Wajnberg et al. extracted implications together with RCA, using generators [START_REF] Wajnberg | Analyse relationnelle de concepts : une méthode polyvalente pour l'extraction de connaissance[END_REF][START_REF] Wajnberg | Concept analysis-based association mining from linked data: A case in industrial decision making[END_REF]. The approach is applied to detect anomalies in manufacturing by aluminum die casting. The relational context is composed of machined parts, problems and the relation generates between parts and problems. Relational attributes and then concepts are built using the existential quantifier. Then in relational attributes, concepts are rewritten using their initial intent (the intent they had at their creation). This rewriting is made recursively.

In this paper, we build the DGB, and we use AOC-posets rather than concept lattices. We rewrite the relational attributes, as inspired by [START_REF] Wajnberg | Analyse relationnelle de concepts : une méthode polyvalente pour l'extraction de connaissance[END_REF][START_REF] Wajnberg | Concept analysis-based association mining from linked data: A case in industrial decision making[END_REF], to analyze the implications. In addition, we compare several encodings of our data to investigate the impact of this encoding on the implication sets.

Conclusion

This paper explores the combination of RCA and the Duquenne-Guigues basis of implications on an environmental knowledge set in order to render knowledge suitable to experts. Our case study gathers information on plants that can replace synthetic pesticides and antibiotics, and be consumed or used in medical care. The guiding research question was to assess whether splitting the datasets could have a positive or negative impact on the implications' readability by the experts. We identified advantages of this splitting to enable the separate analysis of coherent, simpler, implication subsets, not mixing information types. This is strengthened by the relational attribute rewriting that makes the implication easier to read and to interpret.

As future work, we plan to evaluate the impact of using concept lattices and Iceberg rather than AOC-posets for building the implications, as well as using other quantifiers provided by RCA. We will analyze the complete Knomana knowledge base, which includes additional descriptors such as location and plant chemical compounds. Finally, we will post-process the implications. In particular, we plan to present implications by categories and order them by relevance, using standard metrics or metrics specific to the experts' questions. A preliminary work [START_REF] Saoud | Explicit versus Tacit Knowledge in Duquenne-Guigues Basis of Implications: Preliminary Results[END_REF] investigates the potential of using patterns on implication premise and conclusion for categorizing the implications. These patterns are based on multi-valued attributes (before nominal scaling) describing species, genera and families, and on a 'meta-attribute' representing the presence of information on medical or f ood.

  , these two concepts, respectively named C Org 15 and C Org 22, are ordered by inclusion of their object sets from bottom to top, or equivalently by inclusion of their attribute sets from top to bottom. This figure shows that C Org 15 is a subconcept of C Org 22 where C Org 15 introduces genus1, C Org 22 introduces no-medical, C Org 15 inherits no-medical from C Org 22, and C Org 22 inherits pl1 and pl2 from C Org 15.

Fig. 1 .

 1 Fig. 1. Partial view of a lattice family, of the RCF presented in Table 1, with the protection system lattice to the left and an organism one to the right. A plain or dashed arrow represents respectively a subconcept-superconcept relation or a crosslattice link materialized by a relational attribute. Concept C SystP rot 31 groups 6 protection systems (1, 3, 4, 5, 6, 7) using a plant from concept C Org 22, i.e. pl1, pl2, or pl4, not used in medical care. C SystP rot 25, which is a subconcept of C SystP rot 31, groups 4 protection systems (3, 4, 5, 6), informing that they use a plant from genus1 (∃uses(C Org 15)), not used in medical care (∃uses(C Org 22)) to protect a crop from genus6 (∃protects(C Org 13)) against a pest of genus4 (∃treats(C Org 18)).

  I2) and (rewritten I2) stipulate that for the protection systems treating a pest of genus4 (pest1 or pest2 grouped in C Org 18), we then observe the use of one of the plants (pl1, pl2, pl4) grouped in concept C Org 22, these plants not being used in medical care as indicated by C Org 22 intent. Implication (I2) can also be read from: C SystP rot 25 C C SystP rot 31; C SystP rot 25 introduces ∃treats(C Org 18); and C SystP rot 31 introduces ∃uses(C Org 22). The scope (S) of an implication informs on the number of objects verifying the implication premise, the support being the proportion of EF or EFC objects verifying the implication premise: Let Imp = A =⇒ B, we have S(Imp) = |A |. Support(Imp) = S(Imp)/|G|. Fig. 2 summarizes this computation process for the running example.

Fig. 2 .

 2 Fig. 2. Overview of the process for the running example. (1) The AOC-poset is built from FC OrganismInfo. (2) The EFC ProtSystem is built using the relational attributes ∃r(C), where r is uses, treats or protects, and C is a concept from the OrganismInfo AOC-poset. (3) The relational attributes are rewritten for easier reading. (4) and (5) The DGBs of implications are built for FC OrganismInfo and EFC ProtSystem.

Fig. 3 .

 3 Fig. 3. Data model of the three datasets' representations.

Table 1 .

 1 Example of RCF made of 2 FCs (i.e. OrganismInfo and ProtSystem) on the top and 3 RCs (i.e. uses, protects, and treats) on the bottom. The attribute set of FC ProtSystem is empty.

	OrganismInfo genus1 ... genus4 ... genus6 ... no-medical ...	ProtSystem
	plant1 (pl1)	x	...		...		...	x	...	1
	plant2 (pl2)	x	...		...		...	x	...	2
		prot1		...		...	x	...	x	...	3
		prot2		...		...	x	...	x	...	4
		pest1		...	x	...		...		...	5
		pest2		...	x	...		...		...	6
		...								7
	uses pl1 pl2 pl3 pl4 ...	protects ... prot1 prot2 ...	treats ... pest1 pest2 ...
	1		x ...	1		...		...	1	...	...
	2	x	...	2		...		...	2	...	...
	3	x	...	3		... x	...	3	... x	...
	4	x	...	4		... x	...	4	... x	...
	5	x	...	5		...		x ...	5	...	x ...
	6	x	...	6		...		x ...	6	...	x ...
	7		x ...	7		...		...	7	...	...

... ... ... ... ... ... ... ...

Table 2 .

 2 Excerpt of the EFC ProtSystem presenting relational attributes formed with the universal quantifier ∃, a relation (uses, protects, or treats), and a concept from FC OrganismInfo.

	ProtSystem ... ∃uses(C Org 15) ∃uses(C Org 22) ... ∃protects(C Org 13) ... ∃treats(C Org 18) ...
	1	...		x	...		...		...
	2	...			...		...		...
	3	...	x	x	...	x	...	x	...
	4	...	x	x	...	x	...	x	...
	5	...	x	x	...	x	...	x	...
	6	...	x	x	...	x	...	x	...
	7	...		x	...		...		...

Table 3 .

 3 Quantitative description of the RCFs and AOC-posets.

	Representation	Formal context	#objects #attributes #relational attributes	#concepts AOC Poset (initial step)	#concepts AOC Poset (last step)
	OneTable	FC CombinedRoles	721	1113	0	1005	1005
		All formal contexts 1321	1078	2250	751	1750
	TwoTables	EFC ProtSystem	721	0	2250	1	1000
		FC OrganismInfo	600	1078	0	750	750
		All formal contexts 1927	2169	3017	1507	2517
		EFC ProtSystem	721	0	767	1	1000
	Relational	EFC Plant	562	1008	750	700	705
		EFC Pest	29	45	750	36	37
		EFC Crop	15	38	750	20	25
		FC OrganismInfo	600	1078	0	750	750

Table 4 .

 4 Implications (implic.) from the Duquenne-Guigues basis per scope (S) and maximum scope (Smax).

	Representation	Formal context	#implic. S = 0	#implic. S = 1	#implic. S= 2	#implic. S = 3	(avg) #implic. S = [4-10]	(avg) #implic. S >10	S > 0 #total implic.	Smax (#implic.)
	OneTable	FC CombinedRoles 3360	1105	281	125	236 (33.71) 173 (2.34) 1920	721 (1)
		EFC ProtSystem	4891	827	234	95	165 (23.57) 74 (1.90) 1395	721 (1)
	TwoTables	FC OrganismInfo	6069	1007	76	37	42 (7.00)	6 (1.2)	1168	35 (1)
		All FCs	10960	1834	310	132	207	80	2571
		EFC ProtSystem	3414	825	234	95	164 (23.42) 73 (1.87) 1391	721 (1)
		EFC Plant	5698	1509	132	64	85 (14.17) 25 (2.08) 1815	87 (2)
	Relational	EFC Pest	855	67	8	0	4 (2)	1	80	29 (1)
		EFC Crop	740	58	8	4	0	0	70	3 (4)
		FC OrganismInfo	6069	1007	76	37	42 (7)	6 (1.2)	1168	35 (1)
		All FCs	16776	3466	450	208	295	105	4532

  . The DGB contains 70 implications. The small value of Smax (3), indicates that the implications are rather specific. The implications focus on the role of the organisms as crop. A first implication type describes the taxonomy. They come from FC OrganismInf o. A second implication type describes the bijection between the taxonomic information encoded in FCs Crop and OrganismInf o, as the attributes are duplicated in both contexts, completed by information on food and medical care if appropriate. For instance, the following implication (with S = 2) indicates that a crop belonging to family Fabaceae (CrF amily F abaceae) is connected to the OrganismInf o objects representing this family, and is also consumed and not used in medical care:

CrF amily F abaceae =⇒ ∃cr CharactBy(M edical ), ∃cr CharactBy(F ood X), ∃cr CharactBy(F amily F abaceae)

A third implication type informs on the organisms role as crop, such as the following implication (with S = 1) named Rel1, which indicates that crops, used in medical care and not consumed, are from the Ricinus Communis species:

∃cr CharactBy(F ood ), ∃cr CharactBy(M edical X) =⇒ CrSpecies RicinusCommunis, CrGenus Ricinus, CrF amily Euphorbiaceae, ∃cr CharactBy(F amily Euphorbiaceae), ∃cr CharactBy(Species RicinusCommunis&Genus Ricinus) (Rel1)

  OneT able representation The DGB contains 1920 implications. Its Smax value is identical to the one of FCs P rotSystem of T woT ables and Relational. Its S value is lower, and the total number of implications is low (1920), compared to respectively 2571 and 4532 for T woT ables and Relational. This representation thus provides less implications, but with a higher diversity of implication formulations. As illustration, let us consider the implication OT1 that corresponds to Rel1 and TT1 :

	P eF amily N octuidae, M edicalCrop X, F oodCrop =⇒ P eGenus Spodoptera, F oodP lant ,
	M edicalP lant , M ultiU seP lSp , M ultiU seP lGe , M ultiU seP lF a , P lSpIsCrEw , P lGeIsCrEw ,
	P lF amily Asteraceae, P eSpecies SpodopteraLitura, CrSpIsP lEw X,
	CrGeIsP lEw X, P lSpecies W ollastoniaDentata, P lGenus W ollastonia,
	CrSpecies RicinusCommunis, CrGenus Ricinus, CrF amily Euphorbiaceae	(OT1)

Table 4 ,

 4 dividing data into separate FCs, which introduces RCs, produces more implications. This may be explained by the fact that, for a relation (e.g. uses in T woT ables), concepts grouping target objects (e.g. OrganismInf o) induce concepts grouping source objects (e.g. P rotSystem) via the relational attributes. The implications include the result of this propagation schema. As a counterpart, in Relational representation, the implications are divided into coherent subsets, i.e. one per FC, simplifying their analysis. As the examples show, having few or no separate roles limits the relational attribute number and complexity. E.g., an advantage of T woT ables over Relational may be that the T woT ables implications contain one-level relational attributes (one RC), when the Relational ones contain relational attributes composing two RCs. But in return, when reducing the splitting, technical attributes, such as plSpIsCrEw in OneT able (plant species is crop elsewhere), have to be added to express multi-use and role, giving longer implications. This building and the formulation are not easier to understand by the expert. Moreover, as it has been highlighted by T woT ables and OneT able, the less the dataset is split, the more the implications mix information. This situation occurs with organism roles and protection systems, that are mixed in the implications of CombinedRole in OneT able, and of P rotSystem in T woT ables.Threats to Validity. With regard to internal validity, the Knomana knowledge sets have been manually collected by many participants but controlled by two domain experts that are co-authors of this paper. The software used in this evaluation, i.e. RCA algorithms implemented in Cogui and Conexp, have already been used in other case studies with validated results. LinCbO has been implemented in Java and inserted in the Cogui framework. To confirm the correctness of this implementation, the results have been compared with those of Conexp.

http://www.lirmm.fr/cogui/

F ood X means is consumed; F ood means is not consumed, and similarly for M edical X and M edical .

Acknowledgments. This work was supported by the French National Research Agency under the Investments for the Future Program, referred as ANR-16-CONV-0004.