Abductive Reasoning Task

An Abductive Reasoning Task is a non-monotonic reasoning task that requires an abductive argument.

• AKA: Inference to the Best Explanation, Educated Guess, Reasonable Cause, Affirming the Consequent.
• Context:
  • It can be solved by a Abductive Reasoning System by implementing a Abductive Reasoning Algorithm.
  • It can be defined as the task of inferring A as an explanation of B.
  • It can range from being a Logic-based Abduction Reasoning Task, to being a Set-Cover Abduction Reasoning Task, to being a Subjective Logic Abduction Reasoning Task, to being an Abductive Validation Task.
  • It can be based on an Abductive Logic Theory.
  • It can result in an Affirming the Consequent Logic Fallacy.
  • …
• Example(s):
  • Given: 1) Most birds can fly. 2) Only birds are known to fly. 3) Tweety flies. Conclude that: Tweety is a bird.
  • In "detective work" abductive reasoning is used when guesses are made that account for the facts collected to date in order to conclude with "reasonable cause".
  • Given 1) a dataset [math]\displaystyle{ D }[/math], 2) hypothesis [math]\displaystyle{ h }[/math], and 3) [math]\displaystyle{ \nexists \text{ better } h }[/math]; then [math]\displaystyle{ h }[/math] is probably correct.
  • Analogical Reasoning.
  • a Logic-based Abduction Reasoning Task such as:
    • an Abductive Logic Programming Task;
    • a Backward Chaining Task;
  • an Abductive Concept Learning Task;
  • a Subjective Logic Abduction Reasoning Task such as:
    • a Bayesian Inference Task.
  • …
• Counter-Example(s):
  • a Deductive Reasoning Task.
  • an Inductive Reasoning Task.
• See: Non-Monotonic Reasoning, Most Economical Explanation, Explanation-based Learning, Explanation-Based Learning; Inductive Logic Programming, Set Cover Problem, Occam's Razor.

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References

2023

• (Zandie et al., 2023) ⇒ Rohola Zandie, Diwanshu Shekhar, and Mohammad Mahoor. (2023). “COGEN: Abductive Commonsense Language Generation.” In: Proceedings of the 61st Annual Meeting of the Association for Computational Linguistics (Volume 2: Short Papers).
  • QUOTE: ... Reasoning is one of the most important elements in achieving Artificial General Intelligence (AGI), specifically when it comes to Abductive and counterfactual reasoning.
  • QUOTE: ... The abductive inference could be viewed as going backward from the conclusions of a valid deductive inference to the premises to find its plausible causes and effects. In terms of classical logic, this is a fallacy (Andersen, 1973). Abductive reasoning is defeasible (and also non-monotonic) which means the conclusions can be refuted in the light of new data. Although abductive reasoning forms one of the core abilities of human cognition, its research in the area of NLP is still widely unexplored. ...

2022

• (Wikipedia, 2022) ⇒ https://en.wikipedia.org/wiki/Abductive_reasoning Retrieved:2022-4-19.
  • Abductive reasoning (also called abduction, abductive inference, or retroduction ) is a form of logical inference formulated and advanced by American philosopher Charles Sanders Peirce beginning in the last third of the 19th century. It starts with an observation or set of observations and then seeks the simplest and most likely conclusion from the observations. This process, unlike deductive reasoning, yields a plausible conclusion but does not positively verify it. Abductive conclusions are thus qualified as having a remnant of uncertainty or doubt, which is expressed in retreat terms such as "best available" or "most likely". One can understand abductive reasoning as inference to the best explanation, although not all usages of the terms abduction and inference to the best explanation are exactly equivalent. In the 1990s, as computing power grew, the fields of law, computer science, and artificial intelligence research spurred renewed interest in the subject of abduction. Diagnostic expert systems frequently employ abduction.

2022

• (Simple Wikipedia, 2022) ⇒ https://simple.wikipedia.org/wiki/Abduction_(logic)
  • Abduction is the kind of practical logic which answers questions of the type "how did this come about?". It produces answers which are not guaranteed to be correct. Consider the observation that the lawn is wet in the morning. How did that happen? In London, the answer is most often that it rained. But in Los Angeles it is much more likely that someone left the sprinkler on.

    Abduction is logical inference which goes from an observation to a theory which accounts for the observation. It makes the simplest and most likely explanation. In abductive reasoning, unlike in deductive reasoning, the premises do not guarantee the conclusion. Abductive reasoning is "inference to the best explanation".

2017a

• (Stanford Encyclopedia of Philosophy, 2017) ⇒ Stanford Encyclopedia of Philosophy: Abduction http://plato.stanford.edu/entries/abduction/ First published Wed Mar 9, 2011; substantive revision Fri Apr 28, 2017
  • QUOTE: In the philosophical literature, the term “abduction” is used in two related but different senses. In both senses, the term refers to some form of explanatory reasoning. However, in the historically first sense, it refers to the place of explanatory reasoning in generating hypotheses, while in the sense in which it is used most frequently in the modern literature it refers to the place of explanatory reasoning in justifying hypotheses. In the latter sense, abduction is also often called “Inference to the Best Explanation.”

    This entry is exclusively concerned with abduction in the modern sense, although there is a supplement on abduction in the historical sense, which had its origin in the work of Charles Sanders Peirce — see the Supplement: Peirce on Abduction. See also the entry on scientific discovery, in particular the section on discovery as abduction.

    Most philosophers agree that abduction (in the sense of Inference to the Best Explanation) is a type of inference that is frequently employed, in some form or other, both in everyday and in scientific reasoning. However, the exact form as well as the normative status of abduction are still matters of controversy. This entry contrasts abduction with other types of inference; points at prominent uses of it, both in and outside philosophy; considers various more or less precise statements of it; discusses its normative status; and highlights possible connections between abduction and Bayesian confirmation theory.

2017b

• (Kakas, 2017) ⇒ Antonis C. Kakas. (2017). “Abduction”. In: (Sammut & Webb, 2017) DOI:10.1007/978-1-4899-7687-1_1
  • QUOTE: Abduction is a form of reasoning, sometimes described as “deduction in reverse,” whereby given a rule that “A follows from B” and the observed result of “A” we infer the condition “B” of the rule. More generally, given a theory, T, modeling a domain of interest and an observation, “A,” we infer a hypothesis “B” such that the observation follows deductively from T augmented with “B.” We think of “B” as a possible explanation for the observation according to the given theory that contains our rule. This new information and its consequences (or ramifications) according to the given theory can be considered as the result of a (or part of a) learning process based on the given theory and driven by the observations that are explained by abduction. Abduction can be combined with induction in different ways to enhance this learning process.

2001

• (Magnani, 2001) ⇒ Lorenzo Magnani. (2001). “Abduction, Reason, and Science. Processes of Discovery and Explanation.” Springer. ISBN:0306465140

1989

• (Poole, 1989) ⇒ David Poole. (1989). “Explanation and Prediction: an architecture for default and abductive reasoning.” In: Computational Intelligence, 5(2) doi:10.1111/j.1467-8640.1989.tb00319.x

1903

• (Peirce, 1903) ⇒ Charles S. Peirce. (1903), Harvard lectures on pragmatism, Collected Papers v. 5, paragraphs 188–189.

1901

• (Peirce, 1901) ⇒ Charles S. Peirce. (1901). “On the Logic of drawing History from Ancient Documents especially from Testimonies."

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