What did the Buddha mean by the four types of reasoning in his advice to the Kalamas?

In AN 3:65, while advising the Kalamas on how to choose among a variety of contradictory belief systems, the Buddha mentions ten inadequate criteria for truth: > Come, Kalamas. Do not go by oral tradition, by lineage of teaching, by > hearsay, by a collection of texts, **by logic, by inferential > reasoning, by reasoned cogitation, by the acceptance of a view after > pondering it**, by the seeming competence of a speaker, or because you > think, 'The ascetic is our teacher.' I am interested in the four criteria that seem to relate to verbal reasoning (an alternative translation in parentheses): - Logic (surmise) - Inferential reasoning (axiom) - Reasoned cogitation (specious reasoning) - Acceptance of a view after pondering it (bias towards a notion that has been pondered) Bikkhu Bodhi has a footnote that, much to my consternation, says of these criteria, > [They are] four types of reasoning recognized by thinkers in the Buddha's age; their differences need not detain us here. I understand the main point being made (that we should go by direct experience), but I am curious about the precise meaning of these four criteria. **I am looking for an answer that explains the differences between these four types of reasoning by providing an example of each one from everyday life.** Bonus for any relevant historical context.