Abduction: The missing puzzle of AI (Part 1)

“Reasoning” is one of the most important elements in achieving real AI. One of the main differences between the three kinds of reasoning is as below:

1- In deduction, it is impossible that the premises are true and the conclusion would be false. The relationship between premises and the conclusions is of “necessity”. All humans are mortal then all men are mortal.

2- In induction, it is improbable that the premises are true and the conclusion would be false. The relationship between premises and the conclusions is of “probability”. If all the observed swans are white then all swans are white.

3- In abduction, it is implausible that the premises are true and the conclusion would be false. The relationship between premises and the conclusions is of “plausibility”. The knife is in the back of the corpse so it’s plausible that he has been killed (in contrast to suicide or accident)

The third kind of reasoning is the weakest of all.

Charles Pierce Sanders the American mathematician, logician, and philosopher which is known for being the “father of pragmatism” introduced the “abduction” reasoning and tried to develop it. Pierce defined abduction in terms of “explanation” and “hypothesis”. His concise definition reads: “Abduction is the process of forming an explanatory hypothesis”. He even occasionally uses the term “hypothesis” as a synonym for abduction. Thus he saw abduction as prior to induction and deduction in the process of scientific argumentation. Abduction is how the scientist forms the hypothesis that is later tested using deductive or inductive reasoning. This

account makes abduction seem vitally important in scientific methodology. Peirce emphasized the central importance of abduction in science, and he saw it as extremely valuable in the process of scientific discovery. He wrote, “Every single item of scientific theory which stands established today has been due to Abduction.

He points out several characteristics of abduction:

1- it is a technique used to narrow down the number of alternatives by picking out one or a few hypotheses from a much larger number of them that are available.

2- It is a process of guessing or picking the right guess, and thus it is clear that it is a fallible process that can lead to wrong hypotheses as well as to right ones.

3- it comes into play when a new phenomenon is observed, in other words, a phenomenon that has not yet been explained, or explained well enough, in science.

The second characteristic is a bit mysterious. Peirce called abduction “insight” of a kind he equated with “the faculty of divining the ways of Nature.” He theorized that abduction “resembles the instincts of the animals.”

He uses one example that illustrates the three types of reasoning in contrast to each other.

INDUCTION

Premise One: These beans are from this bag.

Premise Two: These beans are white.

Conclusion: All the beans from this bag are white.

this inference is inductive because it goes from the case (premise one) and the result (premise two) to the rule.

By comparison, a deductive inference goes from applying a general rule to a particular case in

order to get a result, as in the following example

DEDUCTION

Premise One: All the beans from this bag are white.

Premise Two: These beans are from this bag.

Conclusion: These beans are white.

Probably the biggest issue with deduction is how to find the general rule in the first place. It could come from induction or some other sources.

ABDUCTION

Premise One: All the beans from this bag are white.

Premise Two: These beans are white.

Conclusion: These beans are from this bag.

The first premise is the rule, the second is the result, and the conclusion is the case, in Peirce’s reconstruction. The line of reasoning in the example can also be reconstructed as follows. On the table, I see a handful of white beans. On further investigation, I find that one bag contains white beans only. These are my findings. They represent the observed facts or empirical data of the case. What could explain these data? Well, a hypothesis that could explain them is that the handful of beans could have come from the bag that was found to contain only white beans.

The deductive inference is abstracted from the data and is independent of them. Inductive inference is based on the data but extrapolates partially beyond them. Abduction extrapolates even further beyond the data. It stretches “quite beyond the limits of our observation; to use Peirce’s terms. Thus abductive reasoning “infers very frequently a fact not capable of direct observation”. To prove his point, Peirce used the example of the hypothesis that Napoleon Bonaparte once existed. In his view, an abductive inference of this kind could never be replaced by inductive inference. It just goes too far beyond the data. This example is quite convincing and helps us grasp what the difference between inductive reasoning and abductive reasoning is supposed to be in the Peircean view.

The abductive inference could be viewed as going backward from the conclusions of a valid deductive inference to the premises. In terms of classical logic, this is a fallacy. A mathematician is trying to determine whether a proposition A is true or not. The mathematician does not know that but does know that A implies B. If B is false, it would follow deductively by modus tollens that A must also be false. However, suppose the person finds that B is true. What would that suggest? According to Polya, there is a heuristic inference: “since its consequent B turned out to be true, A itself seems to deserve more confidence.” Polya did not identify this heuristic inference by using the term “abduction.”

it is good to notice how much abduction depends on a particular view of explanation. Fann, as quoted above, wrote that “to explain a fact is to show that it is a necessary or probable result from another fact, known or supposed.” but when we say it’s more credible the question arises how much?

How should we evaluate the strength or weakness of a given abductive argument? Peirce would presumably have answered that strength and weakness can be evaluated by testing them out by further observations or experiments. Josephson and Josephson presented an answer that basically agrees with Peirce’s theory that abduction needs to be evaluated in light of the process of forming and testing a hypothesis in an inquiry.

According to Josephson and Josephson, the judgment of likelihood associated with an abductive inference should be taken to depend on six factors.

1- how decisively H surpasses the alternatives

2- how good H is by itself, independently of considering the alternatives

3- judgments of the reliability of the data

4- how much confidence there is that all plausible explanations have been considered (how thorough was the search for alternative explanations)

5- pragmatic considerations, including the costs of being wrong and the benefits of being right

6- how strong the need is to come to a conclusion at all, especially considering the possibility of seeking further evidence before deciding.

The collection of more facts may suggest a new explanation that may even be better than the one now accepted. The conclusion is an intelligent guess based on what is known at some given point in an investigation that may, or perhaps even should continue.

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