Logical models

Logical models divide the instance space, that is the set of all possible or allowable, instances, into segments. The goal is to ensure that the data in each segment is homogeneous with respect to a particular task. For example, if the task is classification, then we aim to ensure that each segment contains a majority of instances of the same class.

Logical models use logical expressions to explain a particular concept. The simplest and most general logical expressions are literals, and the most common of these is equality. The equality expression can be applied to all types—nominative, numerical, and ordinal. For numerical and ordinal types, we can include the inequality literals: greater than or less than. From here, we can build more complex expressions using four logical connectives. These are conjunction (logical AND), which is denoted by ∧; disjunction (logical OR), which is denoted by ∨; implication, which is denoted by →; and negation,...