Introduction

At present, competence management finds complications in understanding the real meaning of competence in unstructured digital professional and academic profiles, where its significance depends directly on the knowledge and perception of the publisher. Thus, one of the main limitations is competence interpretation, leading to more than one meaning. For example, we find skills that describe different cognitive levels and processes simultaneously, generating that the publisher determines erroneous assumptions about these skills. In this way, we find ambiguous gaps in the alignment of competence terms, which constitute a natural language problem, affecting the construction of competence models.

In general, the lack of clarity of competencies causes ambivalences and misunderstandings, which do not allow them to create specific training or curricula (Kravcik et al., 2018). An educational syllabus requires definitions of domain and scope of knowledge and skills to acquire competencies (Guevara et al., 2017) correctly. On the other hand, universities require to update academic profiles with new labor market needs (Elchamaa et al., 2019). But if job requirements are ambiguous, how can academic profiles accomplish the desired competencies (Kondratova et al., 2017) and guarantee good validation processes for acquiring competencies (Gluga et al., 2013)? Thus, it is necessary to propose models for competence ambiguity recognition in the professional and academic profiles (Ramsauer, 2020).

Semantic models like ontologies modeling the relationships between skills and knowledge, providing a theoretical and contextual framework for creating professional and academic profiles (Miranda et al., 2017). Despite this, ontologies face lexical ambiguity problems between terms and concepts, causing ambivalences when unifying information from multiple sources (De Leenheer et al., 2007). Furthermore, ontologies use formal languages, such as the Description Logic, to describe concepts and their relationships by assigning them true or false values (Hassan et al., 2012; Malzahn et al., 2013; Montuschi et al., 2015; Sateli et al., 2017; Sikos, 2017), which limits the ability of an ontology to represent the meaning of ambiguous terms (Guo et al., 2016). Consequently, ontologies are not efficient for the representation of competence ambiguity in academic and professional profiles.

On the other hand, dialetheic logic is paraconsistent logic, which considers that logic - formulae can be true, false, or both. Applied to formal models, the arguments (axioms) in dialetheic logic allow contradictions and ambivalences that present several truth values ​​simultaneously (Pulcini, 2018). In this sense, dialetheic logic enables the representation of contradictory or ambivalent events; consequently, dialetheic logic can be a valid alternative to model computationally the ambiguity presented by competencies.

There are investigations where the principles of dialetheic logic are the foundation for solving problems, mainly in decision support (Zamansky, 2019), providing a non-rigid notion of consistency on large knowledge bases and ontologies (Pelletier et al., 2017). On the other hand, there are methods for ontological representation to deal with cases of uncertainty (Dubois, 2012) (Perozo et al., 2013), Vagueness (Lukasiewicz, 2008), and imprecision (Faes, 2019). An extension of description logic is carried out for all of them, defining a set of rules for probabilistic and Vagueness cases without testing in real contexts.

According to Pelletier et al. (2017), lexical ambiguity of five natural language phenomena is related to Vagueness, failure of a presupposition, counterfactual reasoning, fictitious discourse, and contingent statements about the future. Each phenomenon generates contradictions in the statements that make it impossible to obtain a single truth value. These phenomena are presented in the context of professional and academic profiles when publishers create ambivalent phrases according to their knowledge, experience, and beliefs. In this way, professional and academic profiles contain ambiguous competence statements, whose truth values can be true or false or both.

This work aims to develop a knowledge model to analyze the ambiguities of academic and professional profiles from dialetheic logic. First, we identify the cases of ambiguity in the competencies, and then, we create a knowledge model based on dialetheic axioms called the Dialetheic Model (DM). After, we apply the DM over a set of terms of competence belonging to a Competencies Ontology (OC) defined in General Descriptive Logic. Subsequently, using measures of Robustness and Entropy, we analyze the two models OC and DM, to determine their capabilities to recognize dialetheic terms.

Thus, the main contribution of this paper is the proposition of a model to analyze academic and professional competence profiles, using dialetheic logic and description logic, being an essential topic for educational technology. Intelligent educational systems and learning environments can use this DM to improve their reasoning capabilities; by computer-supported learning tools to support the learning processes via their personalization; by instructional design methods, curriculum administration systems, and intelligent tutoring systems to acquire and model the knowledge and skills, among other utilizations. In this way, the model contributes to the development of intelligent educational systems, allowing adequate management and validation of competencies during learning processes, curriculum management, among others.

Background

One of the competence management processes is the construction of professional profiles, which arise the set of competencies of the ideal individual to successfully fill a job position (Guo et al., 2016). With this information, companies plan the training their employees require, and universities develop their academic profiles (Malzhan et al., 2013). Due to the business environment dynamics and the non-standardization of the core competencies of most companies (Elchamaa et al., 2019), the competencies have different interpretations gathering in the job offers. In this way, universities receive ambiguous competencies from the work environment, complicating the alignment between academic and professional profiles (Ramsauer, 2020).

On the other hand, the university degree programs build learners’ competencies, managing the appearance of new positions and the growing need for experts in certain areas (De Leenheer et al., 2007). At the same time, the university must align with learning goals defined in standards and frameworks (e.g., ACM, EQF, etc.) to comply with the regulations of government entities. However, the competencies of these professional bodies vary in their descriptors, granularity, specificity, and structure (Gluga et al., 2013).

The panorama narrated in the previous paragraphs generates ambiguities in the skills and knowledge within the models of competencies (Miranda et al., 2017), and consequently, in the descriptions of the degree programs (Kondratova et al., 2017) and the syllabuses (González et al., 2017). This section describes the theoretical aspects related to this problem and the proposed resolution.

Description Logic and Representation of Competencies

Description logic plays a crucial role in the ontological models that currently support competence management, like OWL Lite and OWL DL (Horrocks et al., 2003). Description logic generally provides the first-order formalism with a well-established and straightforward declarative semantic to capture the meaning of the most popular features of structured knowledge representations (Lukasiewicz, 2008).

However, the Description logic is not reliable for representing the information uncertain, vague or imprecise, which produces inconsistencies in the processes of ontological reasoning due to its inability to handle ambiguity (Sikos, 2017). For instance, it is complicated to describe the existing state, future outcome, or more than one possible outcome when there is incomplete evidence or inconsistent knowledge (Bourahla, 2015).

The ontological models for the management of competencies present Vagueness and uncertainty in their structure at different levels:

  • Terminology: It is impossible to establish what class an individual of the ontology belongs to due to its lexical ambiguity (Malzhan et al., 2013). This case is widespread in those competence models where an ontological population is made from unstructured sources, such as professional profiles (Janev, 2011). For example, in the case of the individual, “software development” may belong to the domain of the concept “application” and the domain of the concept “software” at the same time.

  • Structural: Where concepts’ semantic ambiguity of ontologies causes alignments and mixtures of ontologies that do not present the domain of the analyzed competencies (Gluga et al., 2013). For instance, the concepts “design” and “sketch” are synonymous but may belong to domains of different concepts, such as “knowledge” or “synthesis.“

Consequently, competence management requires efficient, and at the same time, flexible, ontological models for the detection and treatment of ambiguous phenomena.

Dialetheic Logic for the Ambiguity of the Competencies

Formal languages for knowledge representation, such as description logic, cannot show context contradiction cases (Aguilar, 2011; Gutierrez et al., 2017) because their truth values can be either true or false. In contrast, DMs describe linguistic ambiguities through axioms that can be both (Pelletier et al., 2017). For example, the affirmation that a person is in a room when he is walking through the door can say that it is true and false at the same time (Pelletier et al., 2017).

Such assumptions are analyzed by dialetheic logic RM3 through translations of RM3 formulae to classical First-Order Logic (FOL). Defining two translation functions consistent with each other: translation trs (dialetheic truth being true or both) and anti-translation atrs (dialetheic falsity, being false or both) (Pelletier et al., 2017; Sutcliffe & Pelletier, 2019). The unified truth value of the two translations represents the dialetheic possibility that the formula RM3 is both true and false, which confirms the contradiction existing in the formulae analyzed (Arruda, 1980).

Typically, the automated reasoning systems for dialetheic logic can support several languages, such as clause normal form (cnf) and first-order form (fof). Mainly, fof is the language used by the reasoner of RM3 in its internal processes for the translations of RM3 formulae to classical first-order logic (FOL) to use existing first-order reasoning systems (Sutcliffe et al., 2012; Sutcliffe & Pelletier, 2019).

RM3 reasoning analyzes different natural language phenomena, such as term competencies ambiguity, detecting various contradictions defined by formal axioms. Thus, RM3 becomes a viable option for ontological contradiction analysis described by general description logic axioms, especially related to relationships or concepts, due to specific situations defined by the context. For instance, the OC ontology presents ambiguities regarding the knowledge and skill terms caused by the ambiguity of the profiles. The following section explains the axioms in Dialetheic logic applied to competencies ambiguity phenomena in the OC model.

Knowledge Model

The DM model contains hypotheses corresponding to the five dialetheic phenomena: Vagueness, failure of a presupposition, counterfactual reasoning, fictitious discourse, and contingent statements about the future. We apply the descriptions of each axiom on the terms of competence, knowledge, and skill, belonging to documents of a profiles collection analyzed by experts (González-Eras & Aguilar, 2018). These terms belonging to the ontological population of the OC model, following a method developed in (González-Eras & Aguilar, 2019), with the support of knowledge bases of knowledge and skills definitions: DISCO II (for knowledge), BLOOM (for skill) (González-Eras & Aguilar, 2019).

In the following subsections, for each dialetheic phenomenon, we first analyze the axioms using term examples. We present the inference process using natural language and description logic, and finally, the RM3 description is composed of three components: axioms, which correspond to the dialetheic rules that define them; facts, which are the entries to the model from the instances extracted from the digital academic or professional profiles; and conjectures, which are activated during reasoning to perform the interpretation of digital academic or professional profiles (Pelletier et al., 2017).

Vagueness

Vagueness corresponds to a lack of clarity, precision, or accuracy in natural language (Sorensen, 2018). The linguistic patterns of nominal and verbal phrases that identify skills and knowledge competencies may be the same (homonyms). Table 1 shows three examples of the ambivalence of these patterns, which are considered noun phrases of the form NC-SP-NC and NC-SP-NC-AQFootnote 1, representing the knowledge component. However, these terms can be interpreted as a skill (Java expert and Hardware knowledge) or a competence (Software development) (González-Eras & Aguilar, 2019). In this way, the linguistic structure of the nominal phrases is ambivalent, according to the editor’s interpretation of knowledge and skill.

Table 1 Linguistic patterns of vagueness
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In particular, we propose the following axiom for the vagueness problems explained in Table 1:

  • If (the term T has a pattern P as knowledge) and (P is interpreted as a Skill (C1) or Competence (C2)), then (T has an ambivalent pattern).

Figure 1 describes the axiom for the case of the term “hardware knowledge,“ considering the ambiguity in the language patterns of the nominal and verbal phrases for the model’s first axiom, which can be interpreted as knowledge, skill, or competence. According to the facts, the conjecture is true because “hardware knowledge” has a pattern of knowledge. Still, it is interpreted as a skill, which is not understood in the description logic OC model, given its inability to reason about ambivalent facts.

Fig. 1
figure 1

Vagueness analysis process for the term “Hardware Knowledge”

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Table 2 shows the axiom in RM3 format (Dialetheic Logic). As can be seen, the axiom “term hasAmbivalentPattern” establishes the relationship between the linguistic patterns of the terms, depending on whether T (term) has a pattern P that represents knowledge, but that, when it is interpreted is different (as skill (C1) or competence (C2)), so that there is an ambivalence. Thus, although the term linguistic pattern indicates a nominal phrase that corresponds to knowledge, the term is interpreted as a skill or competence.

The model starts with the facts proposal such as fof(hasPattern1, axiom, hasPattern (hardware_knowledge, nc_sp_nc)), on which the axioms perform the interpretations, from basic axioms as fof(isInterpretedAs2, axiom, isInterpretedAs(hardware_knowledge, skill)), until arrives at the conjecture, which is an axiom that interprets the facts based on the basic axiom fof(conjeture1,conjecture,(hasAmbivalentPattern(hardware_knowledge,nc_sp_nc))).

Table 2 Vagueness axioms in RM3 format
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Contingent Statements About the Future

The statements analyze future events, actions, etc. (Peter & Hasle, 2015). This phenomenon occurs in verbal phrases that generally describe competencies and skills. In this case, the phrase is formed by several verbs that, considering their synonyms, are found in different skill levels and cognitive processes, which do not establish what skill the competence will develop shortly. For example, according to the thesaurus Bloom described in González-Eras and Aguilar, (2019), for the competence of Table 3, “Design and manage systems,“ the word “design” belongs to the cognitive level 3 and the word “manage” to the cognitive level 5, both within different cognitive processes (lower and higher, respectively). Therefore, if this competence is eventually needed, it is ambiguous to establish the teaching mechanisms to achieve it. Even the learning evaluation process is unclear at what level and cognitive process must be considered the competence.

Table 3 Cases of contingent statements about the future in profiles terms due to cognitive levels contradiction
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To formalize this contradiction, we propose the following axioms for the contingent statement problems of the examples in Table 3.

  • Problem 1: If (the term Th is synonymous with the thesaurus term Tb) and (Th and Tb have different cognitive levels Nc1 and Nc2), then (Th belongs to several cognitive levels).

  • Problem 2: If (the term Th1 is synonymous with the term Th2) and (Th1 and Th2 belong to different cognitive levels Nc1 and Nc2), then (Th1 and Th2 have several cognitive levels).

  • Problem 3: If (the term T is synonymous with the terms Th1 and Th2) and (Th1 and Th2 belong to different cognitive levels Nc1 and Nc2), then (T has several cognitive levels).

Figure 2 presents the inference process of the axioms, in the case of the term’s “design” and “plan,“ considering the ambiguity between terms of skills when they belong to two different levels and cognitive processes. The reference thesaurus for this analysis is the BLOOM thesaurus explained in González-Eras and Aguilar (2019), in which each cognitive level has associated a set of related terms. So, a term in a given cognitive level can be synonymous with a term that belongs to a different cognitive level. Thus, the term is ambiguous because its synonyms belong to two different cognitive levels and, therefore, to two different cognitive processes.

For example, for the first case, the axiom “termBelongsSeveralCognitiveLevels” establishes that if the term Th is synonymous with Tb, and the cognitive levels of Th (Nc1) and Tb (Nc2) are different, then they can belong to several cognitive levels (Nc1 and Nc2). In this way, the contradiction of term Th is identified on what cognitive level it belongs to; consequently, since Th belongs to several cognitive levels, then it is established that it also belongs to several cognitive processes.

Fig. 2
figure 2

Analysis process of contingent statements about the future in the synonyms “design,“ “plan,“ and “sketch” due to their belonging to different cognitive levels

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In Table 4, we present the DM of the axioms starting with the fact to establish that their cognitive levels are different (with fof(isDifferent2, axiom, isDifferent (synthesis, application))). Then, the synonymy relation is established between the terms (with fof(isSynonymous2, axiom, isSynonymous (design, plan))), and of the membership of each term to a cognitive level (with fof(belongsCognitiveLevel1, axiom, belongsCognitiveLevel (design, synthesis))). In this way, as shown in Fig. 2, the knowledge base for interpretation is built for the conjecture fof(conjecture, conjecture,(termsBelongSeveralCognitiveLevels (design, plan))), which has a value of true because “design” and “plan” are synonymous and belongs to different cognitive levels ( “synthesis” and “application,“ respectively).

Table 4 Axioms of contingent statements about the future in profile terms in RM3 format
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Fictional Discourse (Speech)

According to the people’s beliefs, the statements imply making decisions related to particular real or imaginary assumptions (Eklund, 2017). In the case of competencies and their knowledge and skill components, it is common for the profile editor to place these three components under sections of a document, such as the description, the occupational field, and not precisely as competencies, knowledge, or skills. Table 5 shows some cases founded in (González-Eras & Aguilar, 2019), where the profile editor placed the competence “Plan and manage computer projects” as an antecedent. A similar case concerns of knowledge topic “Industrial process control,“ set in the competence section. Consequently, it depends a lot on the interpretation and knowledge of the editor to recognize a competence or its knowledge and skill components, which can generate a fiction in the writing of the academic or professional profile.

Table 5 Cases of Fictitious speech in profiles terms due to their meaning and location
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In particular, we propose the following axiom for this problem, according to the examples in Table 5. In this case, the description logic fails to represent the contradiction of the facts; for instance, the term “industrial process control” is a knowledge component, but it is located as a competence.

  • If (the term T is located in the section of document C1) and (T is a component C2) and (C1 is different from C2), then (T is a fictitious phrase).

Figure 3 presents the inference process of the axioms for the term “industrial_process_control” and the component “competencies’’, establishing the contradiction in the narrative of a profile. When the term T is located in the section of document C1, being a component of C2, and C1 is different from C2, it causes an unreal statement about the term T. Consequently, the phrase meaning that contains T is altered, generating a fictional speech in the profile. As a consequence, the editor places the competence and knowledge terms under sections with no relationships.

Fig. 3
figure 3

Fictitious phrase analysis process for the term “industrial process control”

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In Table 6, we present the axiom “isFictitiousPhrase” starting with the fact that the term is a component of “knowledge” (with fof(isComponent1,axiom,isComponent( industrial_process_control, knowledge))), which is located in the “competencies” section of the document (with fof(isLocated1, axiom, isLocated (industrial_process_control, competencies))), being different “knowledge” and “competencies” (with fof(isDifferent2, axiom, isDifferent(knowledge, competencies))). Based on the facts, the conjecture fof(conjecture, conjecture, (isFictitiousPhrase (industrial_process_control, competencies)) has a value of true, because at the same time “industrial_process_control” is a “knowledge” component and is identified as a “competence”.

Table 6 Axioms of fictitious terms in RM3 format
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Presupposition Failure

The statement implies the assumption of something that is not really true (Beaver, 1997), applied to competencies when the term is misused in a profile section, in such a way that the term presupposition is wrong. According to the editor’s interpretation, it is of a type, but it is another type. For example, in Table 7, the term “Develop computer applications” is assumed as a “Career profile”, when in fact, it is interpreted as a “Skill” (González-Eras & Aguilar, 2019). Similarly, “Hardware control” is supposedly an “Antecedent,“ being a “Knowledge,“ and so for the other cases. Thus, for each term, the assumption made by the profile editor is wrong concerning the expert’s interpretation.

Table 7 Cases of Presupposition failure due to the contradiction of interpretation by experts of profiles terms
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To formalize this contradiction, we propose the following axiom for this problem, according to the examples in Table 7.

  • If (the term T is located in the section of document C1) and (T has a pattern C2) and (C1 is different from C2), then (T is a Presupposition failure).

Figure 4 presents the inference process of the axioms for the term “java_knowledge” and the description logic model of the axiom of this problem. It does not adequately represent the ambiguity of the term “Java knowledge,“ which has a knowledge pattern and is located/used as a skill. That establishes the contradiction in using the term T, located in the document section C1, having a pattern C2 different from C1. In this way, the profile editor’s assumption about T fails because he misuses the term in the document.

Fig. 4
figure 4

Presupposition failure analysis process for the term “java knowledge”

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In Table 8, we present the axiom in dialetheic logic “isPresuppositionFailure” starting with the fact that the term has a pattern of knowledge “nc_aq” (fof(hasPattern1,axiom,hasPattern(java_knowledge, nc_aq))), which is located in the “experience” section of the document (fof(isLocatedIn 1, axiom, isLocatedIn(java_knowledge, experience))), being different “knowledge” and “experience” (fof(isDifferent 1, axiom, isDifferent(experience, knowledge))). Based on the facts, the conjecture fof(conjetura,conjecture, (isPresuppositionFailure (java_knowledge) )) has a value of true because at the same time “java_knowledge” has a pattern of “knowledge” that is identified as an “experience”.

Table 8 Presupposition failure axioms in RM3 format
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Counterfactual Reasoning

Considering the meaning of the causal statements can be explained in terms of counterfactual conditionals of the form: “If A had not occurred, then C would not have occurred” (Menzies, 2001). In the context of competencies, counterfactual reasoning applies in the assumptions made when aligning terms of competencies with the terms of thesauri according to lexical similarity measures, establishing thresholds to determine the similarities. We will propose the following hypothesis: “A term and a topic of a competence thesaurus belong to the same domain of knowledge when the measure of similarity between them exceeds the limit of 0.45” (González-Eras & Aguilar, 2019). As shown in Table 9, for the three proposed cases, two belong to the same domain because the similarity measure exceeds the threshold of 0.45. But, if we change the limit value to 0.51, we see that only the case “software” versus “Programming” meets the hypothesis. In general, the threshold value is subjective, causing errors and ambivalences in interpreting the belonging of a term of a domain of knowledge.

Table 9 Cases of counterfactual reasoning due to belonging of term to a domain according to a similarity measure
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According to the examples in Table 9, we propose the following axiom for this problem,

  • If (the term T has a measure of similarity Ms with a topic Tr greater than the threshold Us), then (it belongs to the root topic of the thesaurus TD).

Figure 5 describes the operation of the axioms for the case of the term “software.“ In this case, we address the contradiction in belonging a knowledge term to a thesaurus topic due to the thresholds used in the similarity measures. In this case, using DISCO II as a reference thesaurus (González-Eras & Aguilar, 2015; González-Eras et al., 2018). Mainly, the axiom “termBelongsSeveralTopics” requires compliance with the axiom “termBelongsTopic.“ With these relationships, it is described that a term T belongs to several topics of the thesaurus if the measure of similarity is greater than the established threshold.

Fig. 5
figure 5

Counterfactual reasoning analysis process for the terms “software”, “programming”, and “software debugging”

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Table 10 shows the dialetheic axioms for this contradiction, starting with the facts fof(relationMeasure1, axiom, relationMeasure (software, programming, ms0_48, td1)) and fof(relationMeasure 3, axiom, relationMeasure (software, software_debugging, ms0_52, td12) ), which defines that the term “software” has a similarity measure of 0.48 with “programming” and of 0.52 with “software_debugging.“ Another fact is that similarity measures of 0.48 and 0.52 are more significant than the threshold (0.45), and also that the facts “td1” and “td12” are “different.“ In this way, as shown in Fig. 5, the knowledge base for interpretation is built according to the axiom fof(conjecture, conjecture, (termBelongsTopic (software, td12))), which is the base axiom for the conjecture fof(conjecture, conjecture, (termBelongsSeveralTopics (software))). Considering the term “software,” the result is true because “software” belongs to the topics “programming” and “software debugging.“

Table 10 Counterfactual reasoning axioms in RM3 format
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Experimentation

In this section, we will analyze the capacity of our DM model to detect ambiguities in the OC ontology proposed in (González-Eras & Aguilar, 2019). Thus, we first describe the OC and then evaluate its quality using metrics of the ontological scope, particularly the completeness and Robustness (González-Eras & Aguilar, 2018). Later, we analyze the present ambiguities in the OC using DM and compare it with the entropy metric calculated for the OC. The objective is to analyze the professional and academic profiles from two perspectives: the first is the number of relevant terms that each profile contributes to the OC (see Section 4.1); and, the second, to establish the ambiguity that exists in the terms provided by each profile according to the DM, compared with the Entropy of the OC (see Section 4.2). In this way, the description logic complements the DM to analyze the profiles more in-depth (see Section 4.3).

We consider the terms found in the OC ontology, taken for semantic relevance from a corpus of academic and professional profiles regarding the experiment data. Each document is analyzed to detect knowledge and skill terms using linguistic patterns (NC_SP_NC, NC_AQ). Generally, terms belong to profile sections such as description, objectives, roles, and competencies. They are labeled according to the document section where they are found and their real meaning. Thus, the dataset contains information for the processes performed in both models (OC and DM).

The Ontological Model (OC)

To select relevant terms to the ontological population of the OC defined in González-Eras (2019), the dataset elements are aligned with the DISCO II (Tc1,…, Tc15) and BLOOM (Th1,…, Th6) thesauri, comparing the terms of the thesauri against the terms found in the profiles, using two classes of similarity measures. First, using lexical similarity measures, such as Levenshtein and Sorensen Coefficient, comparing pairs of terms at their characters’ level and obtaining those pairs with the most significant similarity (according to the UL threshold). Second, we compare the chosen pairs with the term’s ancestors, siblings, and children of the thesaurus subtree with the pair is aligned, selecting those that obtain the most remarkable similarity. As a final step, we establish a measure of relevance (Score(idi, Cj)) of each term according to its frequency in the collection of profiles (through Okapi BM25 ranking function (Robertson, 2009)); being a chosen term to fill the ontology if it exceeds the relevance threshold (UR >= 0,3). Thus, the term set is obtained to fill the OC (refer to (, 2019) for more detail).

To establish OC quality, we calculate Completeness and Robustness measures to determine if the ontology is complete and robust regarding how many relevant terms have been obtained from the profiles to fill the ontology (González-Eras & Aguilar, 2018).

Completeness

The OC is considered complete regarding the professional profile idi if it contains all relevant terms extracted from this profile (see Eq. (1)).

$$Completeness\left(OC,{id}_{i}\right)=\frac{\sum _{i=1}^{m}Trelevant\left({id}_{i}\right)\cap Terms\left(OC\right)}{\sum _{i=1}^{m}Trelevant \left({id}_{i}\right)}$$
(1)

Where Trelevant(idi) are the terms whose Score(idi,Cj) is in the range defined by the threshold (UR >= 0.3 ) and Terms(OC) are the candidate terms to integrate the OC.

Score(idi,Cj)

The relevance value of a term consists of its position within the collection of analyzed terms. Specifically, the relevance value of a term Cj in the profile idi is given by:

$$Score\left({id}_{i},{C}_{j}\right)=\sum _{j=1}^{n}IDF\left({C}_{j}\right). \frac{f\left({C}_{j},{id}_{i}\right).({k}_{1}+1)}{f\left({C}_{j},{id}_{i}\right)+ {k}_{1}.(1-b+b.\frac{\left|D\right|}{avgdl})}$$
(2)

Where, f(Cj, idi) is the frequency of appearance of the term Cj in the profile idi; |D| is the number of terms in the profile idi; avgdl is the average length of the profiles in the collection; k1 and b are parameters to adjust the length differences of the profiles; IDF(Cj) is the weight given to the term Cj in the collection, and n is the number of profiles in the collection.

Robustness

An OC is robust about the set of professional and academic profiles if its Cj terms are relevant for the profile idi (see Eq. 3).

$$Robustness\left(OC,{id}_{i}\right)=\frac{\sum _{i=1 \&{C}_{j}\in Terms\left(OC\right)}^{m}Score({id}_{i}, {C}_{j})}{\left|Terms\left(OC\right)\right|}$$
(3)

Finally, this paper uses the entropy metric to analyze the information contained in an ontology. The Entropy allows estimating the amount of information that some concepts contribute to a specific target concept (Haque & Chiang, 2019). This paper uses this idea to say that an ontology, when it is very ambiguous, does not contain useful information. So, intuitively we can think that when the Entropy of the ontology decreases significantly, there is less uncertainty in its content.

Entropy

it determines the amount of information that the OC ontology contains. Considering that the terms of the profiles can be ambiguous, the Entropy defines the uncertainty that each profile idi introduces to the OC (Mendonça et al., 2020) (see Eq. (4)).

$${H}_{OC}\left({id}_{i}\right)= {\sum }_{j=1}^{k}P\left({x}_{j}\right){log}_{2}P\left({x}_{j}\right)$$
(4)

Where: P(\({x}_{j}\)) corresponds to the probability of that term \({x}_{j}\in {id}_{i}\) included in the OC (it is a relevant term) is not both true and false, and k is the number of terms in the profile.

We consider that if the value of the Entropy \({H}_{OC}\left({id}_{i}\right)\) is zero, then the profile idi does not introduce uncertainty.

The Dialetheic Model (DM)

The DM model recognizes two types of events: dialetheic terms, which correspond to those in which the axioms return a positive (true) value of truth, and non-dialetheic terms when the axioms give a negative (false) value of truth. Based on these terms, we define for each profile idi, sdji=1 when the DM recognizes the dialetheic event j (ambivalent term). The following measure is used to evaluate the DM:

Robustness

The DM is considered robust concerning a professional or academic profile idi if it recognizes all its dialetheic terms. Equation (5) presents the Robustness measure, where ni represents the number of dialetheic terms in the profile idi.

$$Robustness\left(DM,{id}_{i}\right)= {\sum }_{j=1}^{{n}_{i}}\frac{{sd}_{ji}}{{n}_{i}}$$
(5)

For this calculation, previously, the terms of competence, knowledge, and skill in the profiles are labeled as dialetheic (ambiguous) when they do not match with their linguistic patterns; they are in the wrong section of the document, among other reasons. Otherwise, they are labeled as non-dialetheic terms. These contradictions are due to the appearance of five natural language phenomena in the formulation of competencies in the profiles. For example, fictional narratives contradict the interpretation of a term and its location in the document (for example, profiles 2 to 11). The robustness metric allows determining if all dialetheic terms are recognized. So, with this metric, the capability to recognize dialetheic terms by the DM model is determined.

Finally, it is possible to calculate the proportion of terms recognized by the DM on all relevant terms in the OC (Pr_DM) and compare them with the Entropy. If the proportion of ambiguous cases detected by DM is close to the entropy value of the ontology, then we could say that DM is identifying the ambiguities present in the ontology. Thus, we can evaluate the capability of the DM to detect the ambiguity of an ontology through its dialetheic terms, which a classical approach cannot consider.

Results and Discussion

This section presents the experiment results, validating the OC quality through the completeness and robustness measures explained in Sect. 4.1. Next, the comparison of the results of the DM application in OC and the Entropy of the OC.

Quality of the OC

The quality of the OC was presented in previous works regarding its completeness and Robustness (González Eras, 2018). In general, for 71.44% of the profiles, the ontology has High completeness (0.5 to 1), and for 22.85% of the profiles, Medium completeness (0.3 to 0.5); Low-level completeness (0 to 0.3) corresponds to two profiles (5.71%). Thus, on average, all relevant terms are used to populate the OC, indicating the usefulness of the process. Regarding Robustness, 28.57% of the profiles have a High relevance, while 68.57% have a medium relevance. In this case, the ontological model contains more than 80% of the relevant components of profiles.

We have included this section about the quality of OC to indicate that when using metrics from the domain of description logic, no problems are found in the ontology. In particular, the metrics used say that the competence dataset is well described by the ontological model defined by the OC. However, this ontological model cannot determine if the terms included are contradictory, mainly if they present ambiguities typical of natural language phenomena. A first approximation to clarify the above is to apply the entropy metric to the ontological model.

Quality of the DM

Table 11 presents the results of the robustness measure in the DM for the different phenomena of the natural language studied in this work. Thus, in case 1, 93% of the profiles have robustness values ranging between 0.8 and 1, which indicates that DM recognizes all the terms labeled as dialetheic. This trend is maintained for cases 2, 3, and 4, where around 90% of the profiles have robustness values between 0.8 and 1, indicating DM recognizes the relevant dialetheic terms in the profiles. Also, in case 5, the threshold does not affect the robustness value of each profile, identifying the dialetheic terms in the profiles regardless of the threshold used to determine the relevant terms (which will determine if there are more or fewer terms in the OC). So, this factor that serves to analyze the scalability of DM is well covered by it. Finally, we found profiles in that the robustness measure is maintained for the five cases (id20). The Robustness calculation does not apply in some profiles because they have not labeled dialetheic terms (n/a). For example, id12 and id15 for Case 3; and id 29 for cases 1, 2, 3, and 4. In general, we can conclude that the terms labeled with dialetheic for not following the linguistic patterns, for being in the wrong section of the document, among other reasons, are also recognized by the DM as dialetheic terms.

Table 11 Robustness calculation for the DM
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Comparison of the DM with the Entropy of the OC

Table 12 presents the calculation of the Entropy of the profiles for the OC, where the Entropy is zero when it is considered that all the relevant terms of the profile idi do not introduce uncertainty. The results show that a significant majority tend to zero (between 0.5 and zero).

Also, Table 12 presents terms proportion recognized by the DM on the total of terms relevant in the OC for each profile (Pr_DM(id2)). Regarding this value of the DM, it is zero when it does not recognize the relevant terms as dialetheic (ex. id2), and this measure tends to one when it recognizes a significant number of the terms as dialetheic terms (ex. id13). In this table, our DM follows the entropy metrics. For example, for the profiles id2 and id8 the Entropy of both models is zero, which indicates that there is no uncertainty in the OC, which is detected for Pr_DM when its value is zero that means that the terms are not dialetheic. For the rest of the profiles, both values are close, determining that dialetheic terms correlated with the Entropy of the OC.

This result is fascinating since it indicates that our DM can determine the uncertainty present in an ontology. Also, it allows us to analyze which types of ambiguity are present in the ontology (something that cannot be done with the entropy metric).

Table 12 Comparison between the entropy of the OC and the DM based on the uncertainty of ambiguous terms recognized
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Comparison with Other Works

Table 13 compares our proposal concerning related works selected due to their proposal to model competencies and/or handle the phenomena of lexical ambiguity. For this, we consider the following analysis criteria:

  • The knowledge model establishes the information semantic structure.

  • Competence components considered determining the elements involved in the analysis (for example, skills, knowledge).

  • Disambiguation strategy presents methods to deal with the lexical ambiguity in the information units (synonyms, homonyms, hyponyms, and hypernyms).

  • Thesauri indicate the knowledge bases to support the disambiguation process.

  • Data sources indicate the origin of the information in each work.

  • Metrics validation determines methods to the results verification process.

Table 13 Comparison of our proposal with other works
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Dorn and Pichlmair (2007) present an information system for storing, evaluating, and reasoning students’ competencies at universities based on a competence ontology. The system produces competence profiles for job applications based on HR-XML to enable an exchange of data. Paquette et al. (2012) compare competencies defining according to a structured competence model based on a domain ontology to provide a context for recommendations. Fazel-Zarandi and Fox (2010) present a formal ontology for competence management and consider three reasoning problems related to Human Resources Management: determining the set of skills of an individual, conducting competence gap analysis, and determining whether an individual satisfies a set of requirements. Malzhan et al. (2013) define a human resource manager model based on a conceptual model encompassing the market level, the social context, and the relationships between competencies. This model is the basis for an ontology-based decision support system for human resource managers presented in the same article. Mendonça et al. (2015) study ontology comparison (alignment) strategies based on their similarities. This problem is approached as an optimization one, and they propose an ant colony algorithm for analyzing the multiple ontology combinations. Gil-Vallejo et al. (2018) carry out a comparative analysis of the similarity between the verbal meanings in Spanish in the cognitive and linguistic fields. The results of the comparison show a significant correlation between the verbal similarities of both perspectives. Miranda et al. (2017) propose an ontology-based model for the representation of competencies to support several scenarios. The proposed model integrates representations of job offers and demands to support recruiting initiatives and develop employability strategies. Finally, Gugla et al. (2013) describe the CUSP (Course and Unit of Study Portal) system, which supports the design of degree programs. CUSP exploits a semantic mapping approach that gives a flexible and scalable way to map learning goals from multiple accrediting sources.

Most works use ontologies to represent the knowledge and skill components for the knowledge model, limiting these works to Description logic. Our proposal uses a DM to the recognition of cases of contradiction. We have compared its results against a Description model, and it improves the capabilities of recognition of the context. Many works coincide in analyzing knowledge components, while others examine actions and verbs concerning the components analyzed. Our work considers knowledge, skill, and competence studied from the five natural language phenomena.

Concerning disambiguation strategies, several methods use vector space models with similarity measures and algorithms, which align the components with thesauri to eliminate the ambiguity of the elements analyzed. In our proposal, we also use similarity measures against thesauri. Still, additionally, we carry out a study of the ambiguity of the terms based on dialetheic logic, according to the five cases mentioned in Pelletier et al. (2017), which allows us to obtain another perspective of the academic and professional profiles. Most of the thesauri have target languages like English and German, which is a limitation for analyzing and comparing the competence components in the Spanish language. In our proposal, we consider the multilingualism of DISCO II thesaurus as an advantage to the replicability of our DM, not only in Spanish but in other languages. Regarding the model’s validation, the measures of Robustness and Entropy allow determining the capabilities of our proposal for the management of ambivalence and contradiction. Typically, other works use measures like precision or experts’ criteria.

Conclusions and Future Works

The present work proposes a model for representing ambiguity and contradiction in academic and professional competencies, based on axioms defined for five natural language phenomena: Vagueness, contingent statements about the future, fictional discourse, failure in the presupposition, and counterfactual reasoning. The importance of this analysis is due to the competency’s ambiguity in the academic and labor contexts, difficulty terms alignment, and in this way, to identify common competencies and those that represent new requirements.

Although other investigations use different mechanisms for contradiction analysis, the use of Dialetheic Logic, and specifically RM3, allow identifying the ambiguity of description logic axioms and their representation in a framework of paraconsistency. The axioms of RM3 enable the implementation of dialetheic hypotheses from the Description Logic axioms.

In addition, the metrics determine the ability of DM to recognize dialetheic terms and the uncertainty that these terms bring to the OC model. Consequently, the DM in terms of Robustness shows that it is robust. Regarding the Entropy of OC, understood as an ontology uncertainty measure, the proportion of dialetheic terms recognized by the DM follows that value, which can be interpreted as recognizing that degree of ambiguity in the OC.

The model proposed in this work can be part of automatic systems for developing competencies throughout a career program, supporting the validation and monitoring of the fulfillment of competencies in the curriculum subjects (intelligent tutoring systems). It can also contribute to detecting lexical ambiguities in the standards and frameworks used in the development of degree programs (instructional design systems) and in intelligent learning environments to develop flexible learning paths for students within and across subjects. Thus, our proposal provides a solution for lacking the university’s capacity to control automatic acquisition of job requirements and their integration in the issues throughout the entire degree program.

The results obtained allow the correct interpretation of digital academic and professional profiles. Remarkably, this proposal can be used as an extension of the formal representation of competencies based on Description logic, find ambiguities and contradictions in the skill and knowledge components, and provide a new point of view of professional and academic profiles from the dialetheic logic. The validation of the DM through the measures of Entropy and Robustness allows determining the model’s capability to find the presence of dialetheic events in the profiles.

The model works in a Spanish context for the computer science domain. According to the linguistic characteristics of the language where our model is applied, it can be extended to other languages and fields considering the adaptation of the linguistic patterns, which identify the knowledge, skill, and competence components.

Future work considers integrating the proposed knowledge model with semantic models, such as ontologies based on linked data (Jiménez et al., 2019). Also, context-aware ontologies (Aguilar et al., 2018b) allow a deeper analysis of the competencies using information obtained from the Web (Puerto et al., 2012; Rodriguez et al., 2010). In addition, the generations of new experiments apply the proposed DM in other contexts and areas of knowledge, using thesauri and related knowledge bases, for example, in intelligent learning environments like in (Aguilar et al., 2018a).