# Abductive Logic Programming (ALP)

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## What is abductive logic programming?

Abductive logic programming (ALP) is a high-level knowledge-representation framework that can be used to solve problems declaratively based on abductive reasoning. It extends normal logic programming by allowing some predicates to be incompletely defined, declared as abducible predicates. Problem solving is affected by deriving hypotheses on these abducible predicates (abductive hypotheses) as solutions of problems to be solved.

These problems can be either observations that need to be explained (as in classical abduction) or goals to be achieved (as in normal logic programming).

There are 3 forms of reasoning:

### Deductive reasoning

In this form of reasoning, a person starts with a known claim or general belief, determining what follows. Essentially, the deduction begins with a hypothesis and examines the possibilities within that hypothesis to reach a conclusion. Deductive reasoning has the advantage that, if your original premises are true in all situations and your reasoning is correct, your conclusion is guaranteed to be true. However, deductive reasoning has limited applicability in the real world because there are very few premises that are guaranteed to be true all of the time.

### Inductive reasoning

Inductive reasoning makes broad inferences from specific cases or observations. In this process of reasoning, general assertions are made based on specific pieces of evidence. Scientists use inductive reasoning to create theories and hypotheses. An example of inductive reasoning is, “The sun has risen every morning so far; therefore, the sun rises every morning.” Inductive reasoning is more practical to the real world because it does not rely on a known claim; however, for this same reason, inductive reasoning can lead to faulty conclusions. A faulty example of inductive reasoning is, “I saw two brown cats; therefore, the cats in this neighborhood are brown.”

### Abductive reasoning

Abductive reasoning is based on creating and testing hypotheses using the best information available. Abductive reasoning is used in a person’s daily decision making because it works with whatever information is present—even if it is incomplete information. Essentially, this type of reasoning involves making educated guesses about the unknowable from observed phenomena. Examples of abductive reasoning include a doctor making a diagnosis based on test results and a jury using evidence to pass judgment on a case: in both scenarios, there is not a 100% guarantee of correctness—just the best guess based on the available evidence.

## What is the syntax of abductive logic programming?

Abductive logic programs have three components, where:

• P is a logic program of exactly the same form as in logic programming
• A is a set of predicate names, called the abducible predicates
• IC is a set of first-order classical formulae.

## What is an example of abductive logic programming?

Jury duty decisions are one example of abductive reasoning. Let's say you're a juror, and the defendant looks like the image of the man on the security camera robbing the bank. He stutters and pauses, like he is guilty when answering questions posed by the prosecutor. As a juror on your first day as a member of the jury, you conclude that he is guilty, but you are not sure. Here, you have made a decision based on your observations, but you are not certain it is the right decision.

Daily decision-making is also an example of abductive reasoning. Let's say you're stuck in traffic on the interstate and see ambulance and police lights about a half mile ahead. There is an exit coming up and you could take some backroads and then get back on the interstate after the accident. You listen to the traffic report on the radio. You look and see if the exit looks congested. Taking all the information at hand, you make the decision to stay on the interstate and wait for the accident to clear. You made the best decision you could given all of the observations.

## What is abductive theory?

In an abductive approach, the research process starts with ‘surprising facts’ or ‘puzzles’, and the research process is devoted to their explanation. ‘Surprising facts’ or ‘puzzles’ may emerge when a researchers encounters with an empirical phenomena that cannot be explained by the existing range of theories.

When following an abductive approach, the researcher seeks to choose the ‘best’ explanation among many alternatives in order to explain ‘surprising facts’ or ‘puzzles’ identified at the start of the research process. In explaining ‘surprising facts’ or ‘puzzles,’ the researcher can combine both numerical and cognitive reasoning.

## What is the benefit of abductive logic programming?

While cogent inductive reasoning requires that the evidence that might shed light on the subject be fairly complete, whether positive or negative, abductive reasoning is characterized by lack of completeness, either in the evidence, or in the explanation, or both. A patient may be unconscious or fail to report every symptom, for example, resulting in incomplete evidence, or a doctor may arrive at a diagnosis that fails to explain several of the symptoms. Still, he must reach the best diagnosis he can.

The abductive process can be creative, intuitive, even revolutionary.2 Einstein's work, for example, was not just inductive and deductive but involved a creative leap of imagination and visualization that scarcely seemed warranted by the mere observation of moving trains and falling elevators. So much of Einstein's work was done as a "thought experiment" (for he never experimentally dropped elevators), that some of his peers discredited it as too fanciful. Nevertheless, he appears to have been right-until now, his remarkable conclusions about space-time continue to be verified experientially.

## What is abductive analysis?

Abductive Analysis is a new approach to generate theory from qualitative observations grounded in the work of pragmatist Charles S. Peirce. Abduction should be understood in contrast to the better known processes of induction (finding new cases of existing theories) and deduction (testing an existing theory with new observations).  Abduction is required when you encounter surprising, anomalous observations that do not fit existing theories and need to come up with a new theory to accommodate these observations. It is the most creative form of theorizing. Abductive analysis harnesses the notion of abduction for qualitative researchers, offering methodological guidance on how to structure research to cultivate anomalies findings and to work with such observations to generate theoretical insights.

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