1 Conceptual Analysis as a Computational Linguistics Problem
Conceptual analysis in philosophy can refer, in a technical sense, to the discovery of a priori knowledge in the concepts we share , , . For instance, philosophers will say that “male sibling” is a proper analysis of the concept BROTHER, because it decomposes its meaning into two other concepts: a brother is nothing more and nothing less than a male sibling. Doing so allows us to make explicit knowledge that is a priori, or in other words, knowledge that is not empirical, that can be acquired without observation: for instance, the knowledge that a brother is always a male. In a broader sense, it can refer to the philosophical methods we use to uncover the meaning and use of a concept in order to clarify or improve it , . Given philosophy’s focus on conceptual clarity, the latter has been ubiquitous in practice. These methods usually seek to make explicit key features of the concept under scrutiny, in order to construct an account of it; be it a formalized representation that can be expressed in terms of necessary and sufficient conditions, or a more intuitive and pragmatic account of it.
Among the empirical sources upon which conceptual analysis relies, textual data is one of the most important. While armchair philosophy (which relies on thought experiments and intuitions) helps one give a better account of his or her own concepts, contact with texts provides an essential perspective. As a result, philosophers often build corpora, i.e. databases of texts that likely use or express a particular concept that is undergoing analysis.
In philosophy as elsewhere, corpora need to be broad enough to cover all the types of usages of the concept under scrutiny, lest the analysis fails to be exhaustive. In other disciplines of social science and humanities, the necessity of grounding analysis in corpora has lead researchers to harness text mining and natural language processing to improve their interpretations of textual data. Philosophy, however, has remained untouched by those developments, save for a few projects, .
One important obstacle to the adoption of those methods in philosophy lies in the lack of proper concept models for conceptual analysis. Keyword approaches to identifying concepts can run into ambiguity problems, like polysemy and synonymy. Furthermore, they can only detect explicit concepts, whereas passages where a concept is latent are bound to also interest the analyst. Latent concept approaches, such as latent semantic analysis (LSA)  or latent dirichlet allocation (LDA) , can work to alleviate ambiguity problems and detect latent semantic expressions, but the dimensions they generate (“concepts” in LSA, “topics” in LDA) are thematic, not conceptual. While concepts typically refer to abstract entities or entities in the world, themes, topics and other thematic units are discursive: they can only describe features and regularities in the text.
The problem we address in this paper is that of retrieving textual segments which are relevant to philosophical conceptual analysis. Considering that conceptual analysis is interested in the entire set of textual segments where a queried concept is present in any form, the task at hand is to detect segments whose discourse expresses, implicitly or explicitly, a queried concept. Our concept detection problem distinguishes itself from traditional information retrieval problems in that the aim is to retrieve text segments where the queried concept is present, rather than text segments that are relevant to the queried concept. In the context of a relevance search, the inquirer will look for the minimum number of documents that can give the maximum amount of generic information about the queried concept; for instance, a web search for “brother” will likely return dictionary definitions and the Wikipedia entry for this word. In the context of a presence query, the inquirer will look for all of the documents where the queried concept is present, thus enabling a more subtle understanding of the concept in all its shades. A search for the presence of the concept BROTHER might thus return texts in genetics or inheritance law as well as implicit evocations of brotherly love in a play. On the other hand, this concept detection problem also differs from entity recognition or traditional concept mining, as the concept does not need to be associated with a word or an expression. While these problems focus on one particular way a concept can be expressed, conceptual analysis will be interested in any kind of expression of a concept, be it direct or indirect, explicit or implicit.
As such, in ConceptDetection, we clarify what counts as concept expression for the sake of conceptual analysis, and we distinguish it from other similar notions. In Method, we describe methods to detect a queried concept’s expression in textual segments from a corpus. In Exp, we present how these methods were implemented and tested, including how an annotated corpus was built, and in Results, results are laid out. Finally, in Discussion, results are discussed, in a bid to shed light on the underlying assumptions of the methods employed.
2 Concept Detection
While conceptual analysis can take many forms, it can always be enhanced by taking empirical data into account. Philosophers who set out to make a concept’s meaning explicit through its analysis typically already possess the said concept, and can thus rely on their own intuitions to inform their analysis. However, their analysis can be improved, both in terms of quality and in validity, by being compared with other sources. This explains, for instance, the appeal of experimental philosophy, which has developed in the last 15 years as a way of testing philosophical intuitions using the tools of cognitive and social psychology. However, these inquiries have their limits: the intuitions they aim to capture are restricted to a specific time and scope, as they are provoked in an artificial setting. Textual corpora give us the opportunity to study concepts in a more natural setting, and in broader populations, or in populations which are hard to reach via conventional participant recruitment schemes (experts, authors from past centuries, etc.).
In order to use data from textual corpora, philosophers now have access to the methods and techniques of computer-assisted analysis of textual data. Those methods and techniques are both numerous and diverse, but there are some common characteristics. For instance, they typically involve various steps, which, together, form treatment chains , 
: textual data are preprocessed (cleaning, lemmatisation, etc.) and transformed into suitable representations (e.g. vector-space model); then, specific treatment tasks are performed, and finally their output is analysed and interpreted. Furthermore, concepts must be identified in the text, in order to extract their associations to other features that can be found in textual data, such as words, themes and other concepts.
One way of identifying a concept in the text is to identify textual segments in which it is expressed. This expression can take many forms: it can be a word that explicitly refers to a concept in a very wide variety of contexts ("moose" for MOOSE), a description ("massive North American deer"), or embedded in an anaphoric reference ("the animal that crossed the street", "its habitat"). It can also be expressed in such a way that it is not tied to any specific linguistic expression. For instance, it can appear in the background knowledge that is essential in understanding a sentence (for instance, in talking about property damage that only a moose could have done), or in relation to the ontological hierarchy (for instance, the concept MOOSE can be expressed when talking about a particular individual moose, or when talking about cervidae).
Our objective here is to test methods of identifying such expressions in textual segments. In other words, our goal is to detect, within a corpus, which passages are susceptible to inform our understanding of how the concept is expressed in a corpus. As such, concept detection can be seen as a useful step in a wide variety of computer-assisted conceptual analysis methods. For instance, it can act as a way of reducing the study corpus (i.e., the corpus on which a concepual analysis is based) to make it more digestible to a human reader, or it can signal that the semantic content of the segments where the queried concept is detected is likely to be related to the concept, and thus enable new ways of representing it.
Because conceptual analysis is focused on a concept’s expression in discourse, concept detection is interested in its presence in discourse. This can mean that the concept is explicitly present, and that it can be matched to a word or an expression, but this presence can also be found in other ways. It can be present in the postulates of the argumentation, without which the passage would be impossible to understand. (For instance, talk of incarceration takes on a very different meaning if we lack the concept of sentencing for a crime). It can be a hypernym to an explicit hyponym, if its properties, expressed to the hyponym, are important enough to the discourse content that we can identify the hypernym as a relevant contributor to the proposition. It can be present in the theme that’s being expanded in the passage. It can be referenced using a metaphor or an anaphor. To synthesize, this criterion can be proposed: a concept is expressed in a textual segment if and only if possession of a concept is necessary to understand the content of the segment.
Concept detection is similar to other popular problems and projects that have been developed within NLP. However, important distinctions justify our treating it as a different kind of problem.
For instance, concept detection differs from information retrieval (IR) in that presence, rather than relevance, is what we are looking for. For instance, while IR might be interested in giving priority to text segments where a queried concept is central, this is of little importance to a conceptual analysis, as salient and less salient expressions of a concept are likely to give different yet equally important dimensions of a concept of interest. Conversely, while IR is interested in relevance of a document to a concept even if it is absent, such a rating is meaningless if one is only looking for presence or absence.
It also differs from other tasks which are geared towards presence detection, such as named-entity recognition or coreference resolution. While a concept can be present because a word or expression directly refers to it, it is not absent because no such expression exists in a sentence or another textual unit. In other words, a concept can be present in a text segment even if no single word or expression refers to it. It can be present in virtue of being part of the necessary background knowledge that is retrieved by the reader to make sense of what she or he is reading. Concept detection, as we mean it, should detect both direct and indirect presence of concepts.
3 LDA Methods for Detecting Concepts
The presence of a concept as described in ConceptDetection can therefore be expressed in various ways: direct explicit reference, anaphorical or metaphorical reference, implicit argumentative or narrative structures, etc. In order to detect these different types of presence, one may expect that we should fragment the task of concept detection into more specific tasks attuned to specific types of presence. In other words, we could detect concept presence by running various algorithms of named-entity recognition or extraction, coreference resolution, topic models, etc. Each of these would detect a specific way in which a concept can become present in a text, and we would rule that a concept is present in a text segment if it has been detected with any of the methods employed. However, not only is such an approach potentially very time consuming, it makes it very hard to have a constant concept representation: these various algorithms will accept different types of representations of the queried concept, and as such, it will be hard to guarantee that they are all looking for the same concept.
One way around this problem is to hypothesize that while these various expressions of a concept are expressed in different ways, they may be conditioned in similar ways by latent variables. We suppose, in this way, that topics—i.e. underlying discursive and narrative constructions which structure a text, cf. —are such latent variables that condition the expression of words and concepts alike. For instance, if the topic “family dinner” is present in a text excerpt, it makes it likely for words such as “table”, “mother”, “brother” to be present, and unlikely for words such as “clouds” or “mitochondria” to be present; and in a similar fashion, concepts such as FOOD, BROTHER and MOTHER are likely to be expressed and concepts such as ORGANELLE and CLOUD are likely absent.
Therefore, given a concept expressed as a word that is typically associated with it, we can find topics in which it is expressed, and use those topics to find the textual segments where it is likely to be present.
We implement this approach using two different algorithms for learning an LDA model, one that is based on Hoffman’s online learning algorithm  and one that is based on Griffiths & Steyvers’s Gibbs sampler .
3.1 Online Learning
Blei’s model uses this generative process, which assumes a corpus of documents each of length :
Choose , where , the topic distribution for document
Choose , where , the word distribution for topic
For each of the word positions , where , and :
Choose a topic .
Choose a word
Here, and are parameters of the Dirichlet prior on the per-document topic distributions and on the per-topic word distribution respectively; is the topic distribution for document ; and is the word distribution for topic .
Through online stochastic optimization, the online LDA algorithm learns (the topic distributions for each document) and (the word distribution for each topic). Thus, it is possible to know which topics are likely to be found in each document, and which words are likely to be found for each topic.
Using this information and given a queried concept represented as a word, we can use to find the topics for which it is among the most important words, relatively, and then use to find the documents in which these topics have a non-negligible presence. We thus have a set of documents which are likely to contain the queried concept.
3.2 Gibbs Sampling-LDA
While it uses the same LDA model, Griffiths & Steyvers’s algorithm 
operates very differently. Rather than estimatingand , it learns instead the posterior distribution over the assignments of words to topics , and it does so with the help of Gibbs sampling, thus assigning topics to each word. After a certain number of sampling iterations (the "burn-in"), these assignments are a good indicator of there being a relationship between word and topic, and between topic and document. From them, we can pick the topics have been assigned to a given word in its various instanciations, and retrieve the documents to which these topics have been assigned. Furthermore, when necessary, and can be calculated from the assignments.
3.3 Concept Presence in Topics
We assume that the presence of a concept in a topic is indicated by the presence of a word typically associated with the concept in question. Therefore a topic’s association with a word is indicative of its association with the corresponding concept. The LDA model explicitly links words to topics, but in a graded way: each word is associated with each topic to a certain degree. From this information, we can use various heuristics to rule whether a concept is involved in a topic or not.
In this study, we tested these heuristics:
- Most Likely:
The queried concept is associated to the topic which makes its corresponding word most likely to occur.
- Highest Rank:
The queried concept is associated with the topic in which its corresponding word has the highest rank on the topic’s list of most likely words.
- Top 30 Rank:
The queried concept is associated with the topics in which its corresponding word is among the top 30 words on the topic’s list of most likely words.
- Concrete Assignment:
In the Gibbs Sampling method, individual words are assigned to topics, and word likelihood given a topic is calculated from these assignments. We can thus say that a word is involved in a topic if there is at least one assignment of this topic to this word in the corpus.
Using these heuristics and an LDA model (learned using either Hoffman’s or Griffiths & Steyvers’s method), we can determine for a given concept the topics in which it is involved.
Depending on the learning method, we can then determine which textual segments are associated to a given topic. On one hand, in Hoffman’s method, when a topic is assigned to a segment, there will be a non-zero probability that any given word in the segment is associated with the topic in question. On the other hand, when learning the LDA model using Gibbs Sampling, we’ll consider that a topic is associated to a textual segment if there is at least one word of this segment that is associated with the topic in question.
Thus, from a given concept, we can retrieve the segments in which the concept is likely expressed by retrieving the textual segments that are associated to the topics which are associated to the queried concept.
Algorithms were tested on a French-language corpus of 5,229 decisions from the Cour d’appel du Québec (Quebec Court of Appeal), the highest judicial court in Quebec. Much like philosophical discussions, arguments in juridical texts, and in decisions in particular, are well-developed, and nuances are important, so we can expect concepts to be explained thoroughly and employed with precision. However, there is much more homogeneity in style and vocabulary, and this style and vocabulary are more familiar to the broader public than in typical philosophical works, which facilitates annotation. Thus, court decisions are likely to afford complex conceptual analyses, but lack the difficulties that come with the idiosyncrasies of individual philosophical texts.
Court decisions were divided into paragraphs, yielding 198,675 textual segments, which were then broken down into words and lemmatized using TreeTagger . Only verbs, adjectives, nouns and adverbs were kept, and stopwords were removed.
In order to provide a gold standard against which we could evaluate the performances of the chosen algorithms, annotations were collected using CrowdFlower111http://www.crowdflower.com.
In a first "tagging" step, French-speaking participants were given a textual segment and were instructed to write down five concepts which are expressed in the segment—more specifically, the criterion mentioned in the instructions was that the concept must contribute to the discourse (in French: "propos") expressed in the segment. 25 participants annotated 105 segments in this way, yielding 405 segment annotations for a total of 3,240 segment-concept associations.
Data obtained from this first step can tell us that a concept is present in a segment, but we can never infer its absence from it, as its absence from the annotations could simply mean that the annotator chose to write down five other concepts and had no more place for another one. Therefore, it was necessary to add another step to assess absence.
In the second "rating" step, participants were given a segment and six concepts (from the pool of concepts produced in the tagging step), and were instructed to rate each concept’s degree of presence or absence from 1 (absent) to 4 (present). The degree of presence is meant to give options to the participant to mark a concept as present, but to a lesser degree, if, say, it is not particularly salient, or if lack of context gives way to some doubt as to whether it really is present. Using this strategy, we can get participants to mark the absence of a concept (degree 1 of the scale) in a way that is intuitive even if one has not properly understood the instructions. For our purposes, we assume that CrowdFlower participants mark a concept as absent when they give it a rating of 1, and as present (even if minimally) if they make any other choice. After removing low-quality annotations, we get 104 segments annotated by 37 participants, for a total of 5,256.
In order to ensure that annotations by CrowdFlower participants reflect a genuine understanding of the text, we also recruited legal experts to make similar taggings and judgments and to compare annotations. While the first task was the same for the experts, the second was slightly different in that there were only two options, and in that they were given oral and written instructions to only mark as absent concepts which were definitely absent. This is because the contact we had with these participants made it possible to ensure that instructions were well understood: we did not need to add options to reinforce the idea that a concept is only absent when it is completely and undoubtedly absent. In total, 5 experts tagged 82 text segments in the tagging step, producing a total of 361 tag-segment pairs, and 4 experts rated concepts on 58 segments in the rating step, producing a total of 412 tag-segment pairs.
As Table 1
shows, the distribution is skewed towards presence, which makes Cohen’sa poor choice of metric . Gwet’s AC1 coefficient  was used instead, and it revealed that CrowdFlower participants and legal experts have moderate but above-chance agreement, with a coefficient of 0.30 and -value of less than 0.05 (indicating that there is less than 5% chance that this above-chance agreement is due to random factors)222The scenario on the tagging step does not fit any of the common inter-annotator agreement metrics. Firstly, a single item is given five values for the same property. Secondly, in our annotations, absence of annotation does not mean absence of concept; the converse would have been a common assumption in inter-annotator metrics.
. As the confusion matrix of Table1 shows, the error mostly comes from the fact that CrowdFlower participants seem much more likely to mark concepts as absent than legal experts.
Both LDA algorithms were implemented as described in the previous section. For the online LDA, we have used the implementation that is part of Gensim , and for the Gibbs sampler-LDA, we have adapted and optimized code from Mathieu Blondel . In both cases, we used topics as parameter, because observing the semantic coherence of the most probable words in each topic (as indicated by ) suggests that greater values for yield topics that seem less coherent and less interpretable overall. For the Gibbs sampler-LDA, we did a burn-in of 150 iterations.
The baseline chosen was the keyword heuristic: a concept is marked as present in a segment if the segment contains the word that represents it, and absent if it does not.
Each method was successively applied to our corpus, using, as queries, items from a set of concept-representing words that were both used in annotations from the rating steps and found in the corpus lexicon. In total, this set numbers 229 concepts for the legal experts’ annotations and 808 concepts for the CrowdFlower annotations. Among these, 170 terms are found in both sets of annotations.
|Online LDA||Most Likely||0.06||0.63||0.13||0.03||0.67||0.07|
|Top 30 Rank||0.18||0.60||0.32||0.15||0.61||0.29|
|Top 30 Rank||0.01||0.64||0.03||0.01||0.25||0.04|
Results from the application of the baseline and our methods on all concepts were compared to the gold standards obtained from the rating step using overall precision, recall, and F1-score. They are illustrated in Table 2.
Apart from the Gibbs Sampling-LDA/Highest Rank method, all of the proposed methods improved on the baseline, except for the ones using word rankings among the Gibbs Sampling-LDA methods. This is due in particular to improvements in recall. This is to be expected, as the keyword only targets one way in which a concept can be expressed, and thus appears to be overly conservative.
Among the Gibbs Sampling-LDA methods, Concrete Assignment fares significantly better, but the best overall, both in recall and F1-score, is the Online LDA/Top 30 Rank. On this, experts and non-experts are in agreement.
These results seem to validate this study’s main hypothesis, that is, LDA methods can improve on the keyword heuristic when it comes to detection of concept expression.
This said, recall remains under 20 %, indicating that topic models are still insufficient to detect all forms of expression of a concept. As such, while it is a clear improvement on the keyword heuristic, it would seem to contradict our hypothesis that topic models can be used to detect all sorts of concept expressions.
|Tagging task (step 1)||0.35||0.10|
|Rating Task (step 2)||0.75||0.24|
6.1 Quality of Annotations
While experts’ and non-experts’ annotations are mostly in agreement, there are important discrepancies. Experts’ annotations systematically give better scores to Gibbs Sampling methods, and lower scores to Online LDA methods, than non-experts’. For instance, while the Online LDA/Top 30 Rank method beats the Gibbs Sampling/Assignment method by 0.11 in F1-scores using CrowdFlower annotations, this difference shrinks to 0.4 when using experts’ annotations. These discrepancies, however, can be traced to a difference in types of heuristics employed in the tagging step: CrowdFlower participants are more likely to employ words from the excerpt as annotations (i.e. using the concept BROTHER when the word “brother” is present verbatim in the text segment), which favors the baseline.
In order to give evidence for this claim, we calculated the propensity of a participant to mark as present a tag that is also a word in the text segment. Specifically, we estimated the reuse rate333The reuse rate here is simply the number of tags which are a word in the text segment divided by the total number of tags that are words. Multi-word expressions were excluded because detecting whether they are in the text or not would be complicated. as depicted by Table 3.444Experts’ annotations were ignored because there were too few annotation instances where the queried concept’s keyword was in the textual segment, and, as a result, values for the "Keyword in segment" condition were uninformative. ). As it turns out, in the initial tagging step, CrowdFlower participants are more than three times more likely to write down a word that is present in the text. As participants in the rating step are only rating tags entered by people of the same group, this translates into a similar ratio in the rating task. However, as it seems that in the rating step, participants are less likely to mark as present a word which is not specifically in the text, reuse rate is inflated for both participant groups. As a result, a large majority of one-word annotations by CrowdFlower participants are already in the text, while the reverse is still true of expert annotations.
Thus, when we discriminate between tags that are present in the textual segment and those that are not, we get a much clearer picture (Table 4). In the first case, the best heuristic is still the baseline, with Online LDA methods offering much better results than Gibbs Sampling-LDA methods. But in the second, the baseline is unusable, and while F1-scores of Online LDA methods drop by more than half, Gibbs Sampling-LDA methods stay the same or improve. Having fewer annotations where the concept’s keyword is in the textual segment will penalize the Online LDA methods, but not the Gibbs Sampling-LDA ones.
As such, this discrepancy should not count as evidence against the hypothesis that CrowdFlower annotations are invalidated by their discrepancies with experts’ annotations. However, it suggests that future annotations should control for the ratio of present and absent words in the rating step. Furthermore, it would be useful to test participants of a same group on the same textual segment/concept pair in order to compare in-group inter-annotator agreement with between-group inter-annotator agreement.
|Keyword in segment||Keyword absent|
|Online LDA||Most Likely||0.21||0.13|
|Top 30 Rank||0.67||0.30|
|Top 30 Rank||0.00||0.03|
6.2 Improving on Topic Model Methods
In any case, while it does not solve the problem of retrieving all the textual segments where a concept is expressed, the Online LDA/Top 30 Rank method makes important headway towards a more satisfactory solution. It improves on the keyword heuristic’s F1-score by 0.25 (both when experts’ and non-experts’ annotations are used as gold standard), and, as such, constitutes a clear improvement and a much better indicator of concept presence.
Improvements could be reached by associating different approaches to concept detection, when we know that some methods do better than others in specific contexts. For example, the keyword heuristic does slightly better than Online LDA/Top 30 Rank when the queried concept’s keyword is present in the text, so it could be used in these situations, while the former method could be used in other cases. In fact, this produces a minor improvement (F1-score of 0.33 with the CrowdFlower gold standard, as compared to 0.32 for pure Online LDA/Top 30 Ranks). We can hope that including other methods for other means of expressing a concept can contribute to further improvements.
In this paper, we expressed the problem of concept detection for the purpose of philosophical conceptual analysis, and sought LDA-based methods to address it. In order to evaluate them, we devised an annotation protocol and had experts and non-experts annotate a corpus.
Our results suggest that LDA-based methods and the Online LDA/Top 30 Rank method in particular, can yield important improvements over the keyword heuristic that is currently used as a concept detection heuristic in many contexts. Despite important improvement, it remains a high-precision, low-recall method. However, while more work remains to be done, this indicates that detecting concepts through topics can serve as a general-purpose method for at least some forms of concept expression that are not captured using naive keyword approaches.
As such, we suggest that further research should try to integrate other methods of detecting concept presence in textual data that focus on other means of expressing concepts in texts and discourse.
This work is supported by research grants from the Natural Sciences and Engineering Research Council of Canada (NSERC) and from the Social Sciences and Humanities Research Council of Canada (SSHRC).
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