Reasoning about knowledge
Formal Concept Analysis: Mathematical Foundations
Formal Concept Analysis: Mathematical Foundations
| Hi-index | 0.00 |
What does it take to possess a concept? Behaviour of various degrees of complexity is based on different levels of cognitive abilities. Concept possession ranges between mere stimulus-response schemes and fully developed propositional representations. Both biological and artifical systems can be described in terms of these levels of cognitive abilities, and thus we can meaningfully ask whether a given system has concepts. We regard that question not in terms of behavioural criteria, but from a formal point of view. We focus on the interrelation between a given objective structure of concepts and a subject's representation of that structure. The main question is how much of the structure of the objective side needs to be mirrored subjectively in order to grant possession of concepts. Our approach shows a strong parallel to epistemic logic. There, the objective side can be represented by an algebra of true propositions, and an epistemic subject can represent some of these propositions as what she believes to be true. As in propositional epistemic logic, in an epistemic logic of concepts the main issue is finding adequate closure conditions on the subjective set of representations. We argue that the appropriate closure conditions can be stated formally as closure under witnesses for two types of relationships among concepts: in order for a subject to possess a concept c she has to represent both a sibling and a cousin of c. We thus arrive at a first formally perspicious candidate for a psychologically adequate epistemic logic of concepts.