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 classification tasks: the interdependencies among the attributes that define a concept, the prototype of a concept, and the typicality of the instances.