Classifying Classification

A Logical Approach to Data-Driven Classification

“…The information domains of Horn theories, for instance, are precisely the Scott domains. For both topics see [10,11].…”

“…This results in the inheritance network in Figure 6, which is the partially ordered set of the attribute and object concepts (AOC-poset ). 10 A theory of the data whose information domain coincides with the AOC-poset can be obtained by taking all rules of the complete Λ-free Horn theory and by adding for each concept to be pruned from the concept lattice a rule whose premise is the conjunction of the intent X of the concept and whose conclusion is the disjunction of the conjunctions of its subconcept intents minus X. For example, to eliminate the node with intent {acyclic, neutral} (the unlabeled node on the right of Figure 5), we can add the rule acyclic ∧ neutral small ∨ medium ∨ large, which is clearly true with respect to Table 2.…”

“…The logic of affirmative assertions, which has its origins in domain theory and program semantics [16,1], has proved useful for the study of formal classification as well [10,11]. Its close connection with Formal Concept Analysis [4] has already been observed in [13], where the emphasis was on the classification of linguistic data; see also [15,14].…”