Final answer:
Rule-based inference is associated with deductive reasoning, using general principles to predict specific results. Inductive reasoning is the process of forming general conclusions from specific observations. Both types of reasoning are integral to the scientific method.
Step-by-step explanation:
Rule-based or proof theoretic inference refers to deductive reasoning. This is a form of logical thinking that uses general principles to forecast specific results, proceeding from the general to the particular. A classic example of deductive reasoning in science is predicting changes in the distribution of plants and animals based on the general principle that a warmer climate affects habitats.
Inductive reasoning, on the other hand, involves arriving at a general conclusion from a number of specific observations, moving from particular instances to broader generalizations. Scientists often employ both inductive and deductive reasoning to complement each other in the scientific method, which includes steps such as making observations, defining a problem, formulating hypotheses, conducting experiments, and drawing conclusions.
To answer the student's question directly, rule-based or proof theoretic inference concerns itself with option (a): Deriving conclusions from a set of rules or axioms, related to deductive reasoning.