A Toothful of Concepts: Towards a Theory of Weighted Concept Combination

We introduce a family of operators to combine Description Logic concepts. They aim to characterise complex concepts that apply to instances that satisfy \enough" of the concept descriptions given. For instance, an individual might not have any tusks, but still be considered an elephant. To formalise the meaning of "enough", the operators take a list of weighted concepts as arguments, and a certain threshold to be met. We commence a study of the formal properties of these operators, and study some variations. The intended applications concern the representation of cognitive aspects of classication tasks: the interdependencies among the attributes that dene a concept, the prototype of a concept, and the typicality of the instances

Pink panthers and toothless tigers: three problems in classification

Many aspects of how humans form and combine concepts are notoriously difficult to capture formally. In this paper, we focus on the representation of three particular such aspects, namely overexten- sion, underextension, and dominance. Inspired in part by the work of Hampton, we consider concepts as given through a prototype view, and by considering the interdependencies between the attributes that define a concept. To approach this formally, we employ a recently introduced family of operators that enrich Description Logic languages. These operators aim to characterise complex concepts by collecting those instances that apply, in a finely controlled way, to ‘enough’ of the concept’s defin- ing attributes. Here, the meaning of ‘enough’ is technically realised by accumulating weights of satisfied attributes and comparing with a given threshold that needs to be met

Concept Combination in Weighted Logic

We present an algorithm for concept combination inspired and informed by the research in cognitive and experimental psychology. Dealing with concept combination requires, from a symbolic AI perspective, to cope with competitive needs: the need for compositionality and the need to account for typicality effects. Building on our previous work on weighted logic, the proposed algorithm can be seen as a step towards the management of both these needs. More precisely, following a proposal of Hampton [1], it combines two weighted Description Logic formulas, each defining a concept, using the following general strategy. First it selects all the features needed for the combination, based on the logical distinc- tion between necessary and impossible features. Second, it determines the threshold and assigns new weights to the features of the combined concept trying to preserve the relevance and the necessity of the features. We illustrate how the algorithm works exploiting some paradigmatic examples discussed in the cognitive literature

Towards Knowledge-driven Distillation and Explanation of Black-box Models.

We introduce and discuss a knowledge-driven distillation approach to explaining black-box models by means of two kinds of interpretable models. The first is perceptron (or threshold) connectives, which enrich knowledge representation languages such as Description Logics with linear operators that serve as a bridge between statistical learning and logical reasoning. The second is Trepan Reloaded, an ap- proach that builds post-hoc explanations of black-box classifiers in the form of decision trees enhanced by domain knowledge. Our aim is, firstly, to target a model-agnostic distillation approach exemplified with these two frameworks, secondly, to study how these two frameworks interact on a theoretical level, and, thirdly, to investigate use-cases in ML and AI in a comparative manner. Specifically, we envision that user-studies will help determine human understandability of explanations generated using these two frameworks

Asymmetric Hybrids: Dialogues for Computational Concept Combination

When people combine concepts these are often characterised as “hybrid”, “impossible”, or “humorous”. However, when simply considering them in terms of extensional logic, the novel concepts understood as a conjunctive concept will often lack meaning having an empty extension (consider “a tooth that is a chair”, “a pet flower”, etc.). Still, people use different strategies to produce new non-empty concepts: additive or integrative combination of features, alignment of features, instantiation, etc. All these strategies involve the ability to deal with conflicting attributes and the creation of new (combinations of) properties. We here consider in particular the case where a Head concept has superior ‘asymmetric’ control over steering the resulting concept combination (or hybridisation) with a Modifier concept. Specifically, we propose a dialogical approach to concept combination and discuss an implementation based on axiom weakening, which models the cognitive and logical mechanics of this asymmetric form of hybridisation

Asymmetric Hybrids: Dialogues for Computational Concept Combination

When people combine concepts these are often characterised as “hybrid”, “impossible”, or “humorous”. However, when simply considering them in terms of extensional logic, the novel concepts understood as a conjunctive concept will often lack meaning having an empty extension (consider “a tooth that is a chair”, “a pet flower”, etc.). Still, people use different strategies to produce new non-empty concepts: additive or integrative combination of features, alignment of features, instantiation, etc. All these strategies involve the ability to deal with conflicting attributes and the creation of new (combinations of) properties. We here consider in particular the case where a Head concept has superior ‘asymmetric’ control over steering the resulting concept combination (or hybridisation) with a Modifier concept. Specifically, we propose a dialogical approach to concept combination and discuss an implementation based on axiom weakening, which models the cognitive and logical mechanics of this asymmetric form of hybridisation

Towards Even More Irresistible Axiom Weakening

Axiom weakening is a technique that allows for a fine-grained repair of inconsistent ontologies. Its main advantage is that it repairs on- tologies by making axioms less restrictive rather than by deleting them, employing the use of refinement operators. In this paper, we build on pre- viously introduced axiom weakening for ALC, and make it much more irresistible by extending its definitions to deal with SROIQ, the expressive and decidable description logic underlying OWL 2 DL. We extend the definitions of refinement operator to deal with SROIQ constructs, in particular with role hierarchies, cardinality constraints and nominals, and illustrate its application. Finally, we discuss the problem of termi- nation of an iterated weakening procedure

"Un parco per tutti" (accessibilità e fruibilità)

La finalità della tesi non è solo quella di poter creare un percorso naturalistico accessibile e fruibile alle persone diversamente abili, in un piccolo parco, ma anche quella di suscitare emozioni nei visitatori a far sì che essi possano portarsi dentro questo vissuto. L’esperienza fatta da una persona disabile, durante il periodo dello stage presso il Parco delle Energie Rinnovabili “Fenice” (www.parcofenice.it), situato nella zona industriale di Padova, e più precisamente nell’isola di Terranegra, ha messo in luce la mancanza di un percorso accessibile e fruibile per tutti all’interno di quella porzione di parco denominata Golena. Dopo un’attenta osservazione e riflessione si è arrivati a realizzare il progetto “UN PARCO PER TUTTI”. Questo percorso si sviluppa nella zona golenale con l’aiuto di pannelli didattici, informativi ed espositivi visivo-tattili. Il presente elaborato, infatti, è correlato con il tirocinio che ha permesso di effettuare l’analisi di fattibilità, attraverso l’osservazione e lo studio della zona golenale. Lo stage è stato compiuto con l’aiuto di personale addetto alle visite guidate e di un diario di bordo per le uscite effettuate. A titolo esemplificativo, si allega una “scheda tipo” (allegato n. 1 in appendice), pensata dalla studentessa per una raccolta più sistematica di dati ed informazioni

In a Nutshell: Perceptron Connectives in Knowledge Representation (Extended Abstract)

We present a number of applications of perceptron connectives and threshold operators to enrich knowledge representation based on description logics