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

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