Abstract:
Attributional calculus (AC) is a typed logic system that combines elements of propositional logic, predicate calculus, and multiple-valued logic for the purpose of natural induction. By natural induction is meant a form of inductive learning that generates hypotheses in human-oriented forms, that is, forms that appear natural to people, and are easy to understand and relate to human knowledge. To serve this goal, AC includes non-conventional logic operators and forms that can make logic expressions simpler and more closely related to the equivalent natural language descriptions. AC has two forms, basic and extended, each of which can be bare or annotated. The extended form adds more operators to the basic form, and the annotated form includes parameters characterizing statistical properties of bare expressions. AC has two interpretation schemas, strict and flexible. The strict schema interprets AC expressions as true-false valued, and the flexible schema as continuously-valued. Conventional decision rules, association rules, decision trees, and n-of-m rules all can be viewed as special cases of attributional rules. Attributional rules can be directly translated to natural language, and visualized using concept association graphs and general logic diagrams. AC stems from Variable-Valued Logic 1 (VL1), and is intended to serve as a concept description language in advanced AQ inductive learning programs. To provide a motivation and background for AC the first part of the paper presents basic ideas and assumptions underlying concept learning.
