3203. Introduction to Artificial Intelligence

Issues in Reasoning


Though the AI research in reasoning has produced a lot of results, there are still many remaining issues, and they show the limitation of the traditional "mathematical logic" when applied outside mathematics.


1. Uncertainties

Classical logic (such as first-order predicate calculus) are certain in several aspects, whereas the actual human reasoning is uncertain.

Meaning of term:

Truth of statement: Process of inference:


2. Non-deductive inference

All the inference rules of traditional logic are deduction rules, which are truth-preserving, that is, the truth of the premises guarantee the truth of the conclusion. In a sense, in deduction the information in a conclusion is already in the premises, and the inference rules just reveal what is previously implicit.
For example, from "Robins are birds" and "Birds have feather", it is valid to derive "Robins have feather".

The problem is, in human reasoning, there are other inference patterns (or rules), that are not truth-preserving in the traditional sense.

The above non-deductive rules do not guarantee the truth of the conclusion even when the truth of the premises can be assumed. Therefore, they are not valid rules in traditional logics. On the other hand, it is easy to see that these kinds of inference often happen in everyday thinking, and, especially, they play important roles in learning and creative thinking. If they are not "valid" according to traditional standards, then in what sense they are better than arbitrary guesses?


3. Various paradoxes

Traditional logic, when used outside mathematics, generate conclusions that are different from what people usually do, so the "logically correct" conclusions are sometimes "intuitively wrong". Such a case is often called a "paradox". Attempts to resolve the above issues will be introduced in the following lectures.