Improving navigation in critique graphs

Critique graphs were introduced as a device for analysing the behaviour of conversational recommender systems. A conversational recommender allows a user to critique a recommended product with statements such as "I'd like a similar product to this one, but cheaper". A critique graph is a directed multigraph in which the nodes represent products, and a directed edge between a pair of products represents how a user can move from one product to another by tweaking a particular product feature. It has been shown that critique graphs are not symmetric: if a user critiques a product pi and is presented with product pj , critiquing product pj in the opposite manner does not necessarily return product pi. Furthermore, it might not be possible to reach all products in a catalogue starting from a given product, or as a consequence of a particular critique some products become unreachable. This latter point is quite unsatisfactory since a user would assume that it is possible to explore the full catalogue by critiquing alone. A number of approaches to overcoming this problem have been proposed in the literature. In this paper we propose a novel approach that exploits the critique graph directly. Specifically, the unreachability is a consequence of a critique graph having more than one strongly connected component. We show how the critique graph can be modified in a minor way, thereby modifying the semantics of critiquing for a given catalogue, so that all products are always reachable.