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:

• In classic logic, the meaning of an atomic (or primary) term is determined by its denotation according to an interpretation, therefore it does not change as the system is running. On the contrary, the meaning of a term in the human mind often does not have a clear denotation, and its meaning changes according to experience and context.
Example: What is "game"?
• In classic logic, when a compound (or defined) term is introduced, its meaning is completely determined by its definition, which reduces its meaning into the meaning of its components and the operator/structure that joins the components. On the contrary, the meaning of a compound term in the human mind often cannot be fully reduced to that of its components, though is still related to them.
Example: Is a "blackboard" exactly a black board?
Truth of statement:
• In classic logic, a statement is either true or false, but people often take truth value as a matter of degree.
Example: Is "A bird can fly" true or false?
• In classic logic, the truth value of a statement does not change over time. However, people often revise their beliefs after getting new information.
Example: After learning that Tweety is a penguin, you may change some of your beliefs formed when you only know that it is a bird.
• In classic logic, all useful inference must start with a consistent premise set, because a contradiction can lead to the "proof" of any arbitrary conclusion. On the contrary, the existence of a contradiction in human mind will not make the person to believe an arbitrary statement.
Example: Have you ever had a contradiction in your mind? Do you believe 1 + 1 = 3 at that time?
Process of inference:
• In traditional reasoning systems, inference processes follow (deterministic) algorithms, therefore are predictable, that is, after each step, what will happen next is predetermined. On the other hand, human reasoning processes are often unpredictable, in the sense that sometimes a inference process "jumps" in an unanticipated direction.
Example: Have you ever waited for "inspiration" for your writing assignment?
• In traditional reasoning systems, how a conclusion is derived is accurately explainable and repeatable. On the contrary, a human mind often generates conclusions whose source cannot be backtracked.
Example: Have you ever said "I don't know why I believe that. It's just my intuition"?
• In traditional reasoning systems, every inference process has a pre-specified goal, and the process is terminatable whenever its goal is achieved. However, though human reasoning processes are also guided by various goals, they often cannot be completely achieved.
Example: Have you ever tried to find the goal of your life? When can you stop thinking about it?

### 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.

• Induction produces generalizations from special cases.
Example: from "Robins are birds" and "Robins have feather" to derive "Birds have feather".
• Abduction produces explanations for given cases.
Example: from "Birds have feather" and "Robins have feather" to derive "Robins are birds".
• Analogy produces similarity-based judgments.
Example: from "Swallows are similar to robins" and "Robins have feather" to derive "Swallows have feather".
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?