Attribute Exploration Using Implications with Proper Premises

We propose a variation of the attribute exploration algorithm. Instead of implications with pseudo-intents as premises our approach uses implications with proper premises. It is known that the set of implications with proper premises is complete, but in general it is not minimal in size. This variation will allow us to calculate all implications of a formal context with premise size at most n, for some fixed $n\in\mathbb N$. This is of interest if the attribute set is large and the user requests valid implications with small premises. Other applications can be seen for formal contexts where the maximal premise size of an implication with proper premise is known, for example multivalued contexts scaled by multiordinal scales only.