Theories, models and bases of attribute implications in multi-adjoint concept lattices with hedges

Abstract Modelling knowledge systems is a fundamental challenge nowadays. Logic rules are essential for this goal in order to, for instance, design decision-support systems in artificial intelligence. However, the determination of these logic rules is a complex problem. In this line, Formal Concept Analysis provides a mechanism to automatically compute rules from a relational data set, which are called attribute implications. The difficulty arises from the potentially large number of valid implications derivable from a given data set, as well as the presence of redundant implications. This paper will focus on the theoretical development of the notions of theory, model and the entailment relations between them, which will allow us to elaborate the notion of basis of attribute implications in the multi-adjoint concept lattice framework enriched with truth-stressing hedges. We will explore one of the most common types of bases, which is constructed by means of the so-called pseudo-intents.