Formal Methods Meet XAI: the Tool DEGARI 2.0 for Social Inclusion

Abstract

We exploit the Description Logic TCL in order to develop a diversity-seeking afective recommender system. The tool DEGARI 2.0 (Dynamic Emotion Generator And ReclassIfier) is an explainable, afectivebased, art recommender that allows to classify and to suggest, to museum users, cultural items able to evoke not only the very same emotions of already experienced or preferred objects, but also novel items sharing diferent emotional stances. The system has been tested on the community of deaf people and on the collection of the GAM Museum of Turin, obtaining promising results.

Keywords

• eol>Description Logics
• Nonmonotonic Reasoning
• Explainable AI
• Recommender Systems

1. Introduction

diferent emotions from the ones already experienced via the fruition of other artworks, is based on the notion of perspective taking [ 4 ], i.e. seeing the world (e.g. an exhibition in this case) from other perspectives. Since this approach is used to promote empathy, cohesion and inclusion across social groups, reaching this goal would represent a huge advancement with respect to the current technologies (e.g. like social media or standard recommender systems) that often lead people toward content that fits their own viewpoint, promoting fragmentation and fostering confirmation biases, instead of cohesion, inclusive reflection, and critical thinking.

2. The TCL Logic for Combining Prototypes

The core component of DEGARI 2.0 relies on a probabilistic extension of a Description Logic called TCL (Typicality-based Compositional Logic), introduced in [ 5, 3 ]. This framework allows one to describe and reason upon an ontology with commonsense (i.e. prototypical) descriptions of concepts, as well as to dynamically generate novel prototypical concepts in a knowledge base as the result of a human-like recombination of the existing ones [ 6 ].

The logic TCL is the result of the integration of two main features: (i) the extension of a nonmonotonic Description Logic of typicality ℒ +TR, introduced in [ 7, 8 ], with a distributed semantics based on the DISPONTE semantics of [ 9 ] and restricted to typicality inclusions; (ii) the adoption of a well established heuristics inspired by cognitive semantics for concept combination and generation [ 10 ] where, in order to formalize a dominance efect between the concepts to be combined, for every combination we distinguish: a HEAD, representing the stronger element of the combination (i.e. the one from which we want to inherit more properties in the final output of the combination), and one or more MODIFIERS. In the logic TCL, typical properties can be directly specified by means of a typicality operator T enriching the underlying Description Logic, and a knowledge base can contain inclusions of the form :: T() ⊑ to represent that “typical s are also ”, where is a real number between 0.5 and 1, representing the probability of finding elements of being also . The resulting knowledge base is a triple ⟨ℛ, , ⟩ where ℛ contains standard, rigid inclusions of the form ⊑ (all s are also s), contains typicality inclusions :: T() ⊑ and is the ABox containing facts about individuals, e.g. () ( is a member of concept ). From a semantic point of view, we consider models equipped by a preference relation among domain elements as in [ 7 ], where < means that is “more normal” than , and that the typical members of a concept are the minimal elements of with respect to this relation. An element is a typical instance of a given concept if belongs to the extension of the concept , written ∈ ℐ , and there is no element in ℐ “more normal” than . In order to perform useful nonmonotonic inferences, we consider the stronger semantics introduced in [ 7 ], where entailment is restricted to a class of minimal canonical models, intuitively those minimizing the atypical instances of concepts. The resulting logic corresponds to a notion of rational closure built on the top of ℒ + TR.

The logic TCL extends ℒ + TR with the distribution semantics known as DISPONTE [ 9 ], which is able to deal with probabilities equipping inclusions and allowing us to describe the notion of scenario [ 3 ]: intuitively, a scenario is a knowledge base obtained by considering all rigid properties in ℛ as well as all ABox facts in , but only a subset of typicality properties in . The idea is to assume that each typicality inclusion is independent from each other in order to define a probability distribution over scenarios: roughly speaking, a scenario is obtained by choosing, for each typicality inclusion of , whether it is considered as true of false. Reasoning can then be restricted to either all or some scenarios. We also equip each scenario with a probability, easily obtained as the product, for each typicality inclusion, of the probability in case the inclusion is involved, (1 − ) otherwise. It immediately follows that the probability of a scenario introduces a probability distribution over scenarios, that is to say the sum of the probabilities of all scenarios is 1.

In the logic TCL, in order to deal with the problem of combining prototypical descriptions of concepts as in [ 3 ], we adopt typicality inclusions in order to formalize typical properties for both the HEAD and the MODIFIERS concepts, and then to exploit the DISPONTE semantics in order to select only some typical properties belonging to them characterizing the combined concept. The preferential semantics underlying the logic TCL, together with the HEAD-MODIFIER heuristics, are able to tackle the problem of conflicting properties.

Formally, given a knowledge base = ⟨ℛ, , ⟩ and given two concepts and occurring in , our logic allows one to define the compound concept as the combination of the HEAD and the MODIFIER , where ⊑ ⊓ and the typical properties of the form T() ⊑ to ascribe to the concept are obtained in the set of scenarios that: 1. are consistent; 2. are not trivial, in the sense that the scenarios considering all typical properties of the HEAD that can be consistently ascribed to are discarded; 3. are those giving preference to the typical properties of the HEAD (with respect to those of the MODIFIER ) with the highest probability. The set of scenarios remaining are those selected by the logic TCL as the result of the procedure. The knowledge base obtained as the result of combining concepts and into the compound concept is called -revised knowledge base: = ⟨ℛ, ∪ { : T() ⊑ }, ⟩, for all such that T() ⊑ belongs to the selected scenario(s).

3. The tool DEGARI 2.0

DEGARI 2.0 exploits the logic TCL in order to provide an ontological formalization of the circumplex theory of emotions devised by the cognitive psychologist Robert Plutchik [ 11 ], [ 2 ]. According to this theory, emotions, and their interconnections, can be represented on a wheel, in which the afective distance between diferent emotional states is a function of their radial distance. The Plutchik’s ontology, formalizing such a theory, encodes emotional categories in a taxonomy, representing: basic or primary emotions; complex (or compound) emotions; opposition between emotions; similarity between emotions. In particular, by following Plutchik’s account, complex emotion are considered as resulting from the composition of two basic emotions (where the pair of basic emotions involved in the composition is called a dyad). The compositions occurring between similar emotions (adjacent on the wheel) are called primary dyads. Pairs of less similar emotions are called secondary dyads (if the radial distance between them is 2) or tertiary dyads (if the distance is 3), while opposites cannot be combined.

The information about the emotional concepts and their corresponding features to combine via TCL are extracted from the NRC Emotion Intensity Lexicon [ 12 ]: such lexicon provides a list of English words, each with real-values representing intensity scores for the eight basic emotions of Plutchik’s theory. The intensity scores were obtained via crowd-sourcing, using best-worst scaling annotation scheme. This lexicon associates words to emotional concepts in descending order of emotional intensity and, for our purposes, we considered the most intensively associated terms for each basic emotion as typical features of such emotion. In this way, the prototypes of the basic emotions were formed, and the TCL reasoning framework is used to generate the compound emotions. Such prototypes of basic emotions are formalized by means of a TCL knowledge base, whose TBox contains both rigid inclusions of the form

BasicEmotion ⊑ Concept , in order to express essential desiderata but also constraints, as an example Joy ⊑ PositiveEmotion as well as prototypical properties of the form

:: T(BasicEmotion) ⊑ TypicalConcept , representing typical concepts of a given emotion, where is a real number in the range (0.5, 1], expressing the frequency of such a concept in items belonging to that emotion: for instance, 0.72 :: T(Surprise) ⊑ Delight is used to express that the typical feature of being surprised contains/refers to the emotional concept Delight with a probability/degree of belief of the 72%.

Once the association of lexical features to the emotional concepts in the Plutchik’s ontology is obtained and the compound emotions are generated via the logic TCL, the system is able to reclassify the cultural items in the novel formed emotional categories. Intuitively, an item belongs to the new generated emotion if its metadata (name, description, title) contain all the rigid properties as well as at least the 30% of the typical properties of such a derived emotion. The 30% threshold was empirically determined: i.e., it is the percentage that provides the better trade-of between over-categorization and missed categorizations [ 13, 14 ].

4. Conclusions

We have tested DEGARI 2.0 with members of Istituto dei Sordi and on the collection of the GAM Museum of Turin. The experiments provided in [ 1 ] show that the efort of tackling diversity-seeking, afective-based and explainable museum recommendations received a moderate, improvable, acceptance from the deaf community. This is an encouraging result considering the challenge of the cognitive barriers involved in the process of the accepting suggestions that do not fit one’s own preferences and viewpoints.

Experiments concerning the perceived explainability of the provided categorization lead to some key elements emerged as guidelines to design and improve the next generation of inclusive and transparent AI systems, potentially going beyond the specific needs of the deaf community. In this regard, it is important to point out how state of the art neural systems and language models, like SenticNet 7, do not have, as a built-in, this feature. It represents, however, one of the major requirements for modern AI systems interacting with the humans (see the recent General Data Protection Regulation (GDPR) that emphasized the users’ right to explanation [ 15 ]).

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