Primitive concepts, tags and rules. The ontology is designed to quantify the association between products and preferences, e.g. to what extent a certain product is for a vegetarian diet, fair trade etc. To measure such associations, we introduce a common alphabet of characteristics for products and preferences. This alphabet is a set of keywords (tags) that represent primitive concepts. They form the semantic space and scope of sustainability. Subsets of these primitive concepts compose a vocabulary of product and preference tags, while a primitive concept is not further decomposed to keep the ontology practical and consistent [48] within its scope, i.e. a primitive concept is regarded disjoint within a chosen scope of sustainability. For example, the preference tag ‘vegan’ can be composed by the two primitive concepts ‘production with no animals’ and ‘production with no animal products’. Moreover, products and preference tags are assigned to products and preferences respectively based on logical rules. For instance, to assign the product tag ‘low fat’ to a product, a logical rule could determine the number of grams of fat, relative to the total product weight, contained in the product and/or whether the product has a low-fat label. Over 600 such rules are created for this purpose using the Drools framework [49]. We focused on food products. They are the ones that populate the knowledge-base and connect to product tags. In summary, the design of the ontology consists of (i) the choice of the primitive concepts, (ii) their assembly to product and preference tags, and (iii) the creation of logical rules to connect the tags with products and preferences. These actions required domain knowledge from experts (WWF, Greenpeace, Ethical Consumer, VKI), reliable data sources (e.g. EU reports) as well as the wisdom of the crowd by running the Social Impact Data Hack [50] to mine and structure information from Wikipedia, for instance, branding information (see electronic supplementary material, § SM.4).

Association scores. The association between a product and a preference tag is measured by their shared primitive concepts that satisfy a preference tag. We distinguish between positive and negative associations by determining for each pair of product and preference tags subsets of primitive concepts that semantically support or oppose the preference tag, i.e. the preference tag ‘vegan’ supports the primitive concept ‘no animals involved in production’ but opposes the concept ‘animal product’. Therefore, the association score comes with positive and negative values in the range [ − 1, 1] by summing up the associations between supported and opposed primitive concepts (see electronic supplementary material, § SM.2 for more details).

Reduction design principle. The construction of product and preference tags should adhere to the reduction design principle: (i) between two tags with the same primitive concepts, one and only one should be assigned to a product or preference, and (ii) when two tags assigned to a product or preference share primitive concepts, these primitive concepts should be removed and form a new tag. In the example of figure 5, the reduction design principle is violated if the product tag AC is assigned to the product, or, the preference tag BC is assigned to the preference. We prove in electronic supplementary material, § SM.1 how this principle minimizes the error of overlapping tags when the association scores are aggregated to calculate the rating of a product. Violations of the reduction design principle may result in excessive influence of certain preferences on the product rating. In practice, these artefacts may be captured by consumers, whose adjustments of preferences provide additional countermeasures against the error of semantically overlapping tags.

Calculation of the sustainability index using the ontology of products and preferences. Assume an alphabet of primitive sustainability concepts represented in this simple example by {A, B, C}. Combining the primitive concepts results is the word vocabulary {A, B, C, AB, AC, BC, ABC} of product and preference tags. Using rules based on experts’ knowledge and verified data such as ingredients of products, the product tags A and C are assigned to a product. Similarly, a sustainability preference is designed by a composition of the two preference tags C and AB. We can now calculate the association scores between the product and preference tags in an automated way (without expert knowledge) by taking the intersection of the tags sets as follows: |{A}{C}|/|{C}|=0, |{C}{C}|/|{C}|=1, |{A}{AB}|/|{AB}|=0.5, |{C}{AB}|/|{AB}|=0. The sustainability index of a product for a given preference is calculated by the average normalized aggregate association scores of the assigned preference tags as demonstrated in this numerical example. The equation labels refer to the equations in electronic supplementary material, §SM.1.

Experts’ guideline. We propose a high-level guideline to populate the sustainability knowledge-base according to the proposed ontology. This guideline can be used by domain experts to guide the construction process and is outlined as follows:

Identify relevant primitive concepts based on (i) the product categories, (ii) the available product data, and (iii) the scope of sustainability preferences (goals).

Create product and preference tags using the primitive concepts such that these tags represent how product/preference characteristics oppose or support a product/preference.

Create rules that connect the product tags with products, and the preference tags with preferences.

Apply the reduction design principle between all combinations of product tags and preference tags that have overlapping concepts.

Calculate association scores between product-preference tag pairs in the range [−1, 1].

If necessary, go back to Step 1, add or remove primitive concepts and repeat the process.

In Step 1, experts determine the scope of the sustainability by defining primitive concepts that capture key characteristics of products and preferences. Experts need to be aware of the products for which they design the ontology, the available information they have about these products as well as the sustainability preferences that should be captured. In Step 2, they can start combining these concepts into tags with the purpose of representing support or opposition to product characteristics and preferences. In Step 3, experts can assign these tags to product and preferences and can formalize rules under which these assignments are made. The processes of the first three steps are the most tedious ones and require knowledge, experience and a good overview of the available information. As an example of facilitating such processes, we performed workshops with several stakeholders during the project lifetime and organized the Social Impact Data Hack [50]. Step 4 applies the reduction design principle to improve the consistency of the ontology. Step 5 performs the calculations of the association scores based on the (automated) calculations illustrated in figure 5. In practice, these calculations are often calibrated by experts to reason about the association scores based on ground truth knowledge. For instance, consider a study that shows evidence about the effect of different preservatives on health. Obviously, the cause of such effects may be related to chemical or biological phenomena at a very low granularity level that is not captured within the scope of the designed sustainability ontology. In this case, association scores measuring can be calibrated to reflect the relative effect of preservatives according to the findings of such a study. Finally, the process can repeat by adding or removing primitive concepts. The motivation for this iterative process is to better capture the whole range of preferences, decompose further primitive concepts to make the ontology more granular, add/remove rules, expand product categories or enrich the knowledge-based with new datasets. During the ontology design, we performed over 10 iterations for validation purposes and the quality criterion for convergence was how well the product rating could be justified to consumers during the preliminary living laboratory tests.

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