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Abduction, or inference to the best explanation, is a method of reasoning in which one chooses the hypothesis that would, if true, best explain the relevant evidence. Abductive reasoning starts from a set of accepted facts and infers to their most likely, or best, explanations. The term abduction is also sometimes used to just mean the generation of hypotheses to explain observations or conclusions, but the former definition is more common both in philosophy and computing. Image File history File links Mergefrom. ... After obtaining results from an inference procedure, we may be left with multiple assumptions, some of which may be contradictory. ... For other uses, see Reason (disambiguation). ... For the trade organisation, see Federation Against Copyright Theft. ... An explanation is a statement which points to causes, context, and consequences of some object, process, state of affairs, etc. ... Look up Hypothesis in Wiktionary, the free dictionary. ... For other uses, see Philosophy (disambiguation). ... RAM (Random Access Memory) Look up computing in Wiktionary, the free dictionary. ...

Deduction, induction, and abduction

(see also logical reasoning) The three methods for logical reasoning, deduction, induction, and abduction can be explained in the following way (taken from [1]): Given α, β, and the rule R1 : α ∴ β Deduction is using the rule and its preconditions to make a conclusion (α ∧ R1 ⇒ β). Induction is learning...

Deduction 

allows deriving b as a consequence of a. In other words, deduction is the process of deriving the consequences of what is assumed. Given the truth of the assumptions, a valid deduction guarantees the truth of the conclusion.

Induction 

allows inferring some a from multiple instantiations of b when a entails b. Induction is the process of inferring probable antecedents as a result of observing multiple consequents.

Abduction 

allows inferring a as an explanation of b. Because of this, abduction allows the precondition a of “a entails b” to be inferred from the consequence b. Deduction and abduction thus differ in the direction in which a rule like “a entails b” is used for inference. As such abduction is formally equivalent to the logical fallacy affirming the consequent. Therefore abductive reasoning is like Post hoc ergo propter hoc as the cause is questionable.

Deductive reasoning is the kind of reasoning where the conclusion is necessitated or implied by previously known premises. ... This article is about logical implication. ... Affirming the consequent is a logical fallacy in the form of a hypothetical proposition. ... The West Wing, see Post Hoc, Ergo Propter Hoc (The West Wing). ...

Logic-based abduction

In logic, explanation is done from a logical theory T representing a domain and a set of observations O. Abduction is the process of deriving a set of explanations of O according to T and picking out one of those explanations. For E to be an explanation of O according to T, it should satisfy two conditions: Logic (from Classical Greek λόγος logos; meaning word, thought, idea, argument, account, reason, or principle) is the study of the principles and criteria of valid inference and demonstration. ... An explanation is a statement which points to causes, context, and consequences of some object, process, state of affairs, etc. ... In mathematics, the domain of a function is the set of all input values to the function. ...

• O follows from E and T;

• E is consistent with T.

In formal logic, O and E are assumed to be sets of literals. The two conditions for E being an explanation of O according to theory T are formalized as:

;

is consistent.

Among the possible explanations E satisfying these two conditions, some other condition of minimality is usually imposed to avoid irrelevant facts (not contributing to the entailment of O) being included in the explanations. Abduction is then the process that picks out some member of E. Criteria for picking out a member representing "the best" explanation include the simplicity, the prior probability, or the explanatory power of the explanation. Wikiquote has a collection of quotations related to: Simplicity Simplicity is the property, condition, or quality of being simple or un-combined. ... A prior probability is a marginal probability, interpreted as a description of what is known about a variable in the absence of some evidence. ...

Abductive logic programming is a computational framework that extends normal logic programming with abduction. It separates the theory T into two components, one of which is a normal logic program, used to generate E by means of backward reasoning, the other of which is a set of integrity constraints, used to filter the set of candidate explanations. Abductive Logic Programming is a high level knowledge-representation framework that allows us to solve problems declaratively based on abductive reasoning. ... Logic programming (which might better be called logical programming by analogy with mathematical programming and linear programming) is, in its broadest sense, the use of mathematical logic for computer programming. ... Backward reasoning (or goal-oriented inference) is an inference method used in artificial intelligence. ...

Set-cover abduction

A different formalization of abduction is based on inverting the function that calculates the visible effects of the hypotheses. Formally, we are given a set of hypotheses H and a set of manifestations M; they are related by the domain knowledge, represented by a function e that takes as an argument a set of hypotheses and gives as a result the corresponding set of manifestations. In other words, for every subset of the hypotheses , their effects are known to be e(H').

Abduction is performed by finding a set such that . In other words, abduction is performed by finding a set of hypotheses H' such that their effects e(H') include all observations M.

A common assumption is that the effects of the hypotheses are independent, that is, for every , it holds that . If this condition is met, abduction can be seen as a form of set covering. The set cover problem (also set covering) is a classical question in computer science and complexity theory. ...

History of the concept

Historically, Aristotle's use of the term epagoge has referred to a syllogism in which the major premise is known to be true, but the minor premise is only probable. A syllogism (Greek: — conclusion, inference), usually the categorical syllogism, is a kind of logical argument in which one proposition (the conclusion) is inferred from two others (the premises) of a certain form. ...

The philosopher Charles Peirce introduced abduction into modern logic. In his works before 1900, he mostly uses the term to mean the use of a known rule to explain an observation, e.g., “if it rains the grass is wet” is a known rule used to explain that the grass is wet. In other words, it would be more technically correct to say, "If the grass is wet, the most probable explanation is that it recently rained." Charles Sanders Peirce (IPA: /pɝs/), (September 10, 1839 – April 19, 1914) was an American polymath, physicist, and philosopher, born in Cambridge, Massachusetts. ... Äž: For the film, see: 1900 (film). ...

He later used the term to mean creating new rules to explain new observations, emphasizing that abduction is the only logical process that actually creates anything new. Namely, he described the process of science as a combination of abduction, deduction and implication, stressing that new knowledge is only created by abduction.

This is contrary to the common use of abduction in the social sciences and in artificial intelligence, where the old meaning is used. Contrary to this use, Peirce stated that the actual process of generating a new rule is not “hampered” by logic rules. Rather, he pointed out that humans have an innate ability to infer correctly; possessing this ability is explained by the evolutionary advantage it gives. Peirce's second use of 'abduction' is most similar to induction. The social sciences are groups of academic disciplines that study the human aspects of the world. ... AI redirects here. ... This article is about evolution in biology. ... Induction or inductive reasoning, sometimes called inductive logic, is the process of reasoning in which the premises of an argument support the conclusion, but do not ensure it. ...

Norwood Russell Hanson, a philosopher of science, wanted to grasp a logic explaining how scientific discoveries take place. He used Peirce's notion of abduction for this ^[1]. Norwood Russell Hanson (1925 – 1967) was a philosopher of science. ... The philosophy of science is the branch of philosophy which studies the philosophical foundations, presumptions and implications of science both of the natural sciences like physics and biology and the social sciences such as psychology and economics. ...

Further development of the concept can be found in Peter Lipton's "Inference to the Best Explanation" (Lipton, 1991).

Applications

Applications in artificial intelligence include fault diagnosis, belief revision, and automated planning. The most direct application of abduction is that of automatically detecting faults in systems: given a theory relating faults with their effects and a set of observed effects, abduction can be used to derive sets of faults that are likely to be the cause of the problem. AI redirects here. ... Diagnosis (from the Greek words dia = by and gnosis = knowledge) is the process of identifying a disease by its signs, symptoms and results of various diagnostic procedures. ... Belief revision is the process changing beliefs to take into account a new piece of information. ... Automated planning is a subfield of Artificial Intelligence concerned with developing computer algorithms to generate plans, typically for execution by a robot or other agent. ...

Abduction can also be used to model automated planning ^[2]. Given a logical theory relating action occurrences with their effects (for example, a formula of the event calculus), the problem of finding a plan for reaching a state can be modeled as the problem of abducting a set of literals implying that the final state is the goal state. Automated planning is a subfield of Artificial Intelligence concerned with developing computer algorithms to generate plans, typically for execution by a robot or other agent. ... The event calculus is a logical language for representing and reasoning about actions and their effects first presented by Robert Kowalski and Marek Sergot in 1986. ...

Belief revision, the process of adapting beliefs in view of new information, is another field in which abduction has been applied. The main problem of belief revision is that the new information may be inconsistent with the corpus of beliefs, while the result of the incorporation cannot be inconsistent. This process can be done by the use of abduction: once an explanation for the observation has been found, integrating it does not generate inconsistency. This use of abduction is not straightforward, as adding propositional formulae to other propositional formulae can only make inconsistencies worse. Instead, abduction is done at the level of the ordering of preference of the possible worlds. Belief revision is the process changing beliefs to take into account a new piece of information. ...

In the philosophy of science, abduction has been the key inference method to support scientific realism, and much of the debate about scientific realism is focused on whether abduction is an acceptable method of inference. Philosophy of science is the study of assumptions, foundations, and implications of science, especially in the natural sciences and social sciences. ... Scientific realism is a view in the philosophy of science about the nature of scientific success, an answer to the question what does the success of science involve? The debate over what the success of science involves centers primarily on the status of unobservable entities (objects, process and events) apparently...

In historical linguistics, abduction during language acquisition is often taken to be an essential part of processes of language change such as reanalysis and analogy ^[3]. Historical linguistics (also diachronic linguistics or comparative linguistics) is primarily the study of the ways in which languages change over time. ... Language change is the manner in which the phonetic, morphological, semantic, syntactic, and other features of a language are modified over time. ... Analogy is both the cognitive process of transferring information from a particular subject (the analogue or source) to another particular subject (the target), and a linguistic expression corresponding to such a process. ...

References

• Awbrey, Jon, and Awbrey, Susan (1995), "Interpretation as Action: The Risk of Inquiry", Inquiry: Critical Thinking Across the Disciplines, 15, 40-52. Eprint

• Edwards, Paul (1967, eds.), "The Encyclopedia of Philosophy," Macmillan Publishing Co, Inc. & The Free Press, New York. Collier Macmillan Publishers, London.

• Eiter, T., and Gottlob, G. (1995), "The Complexity of Logic-Based Abduction, Journal of the ACM, 42.1, 3-42.

• Harman, Gilbert (1965). "The Inference to the Best Explanation," The Philosophical Review 74:1, 88-95.

• Josephson, John R., and Josephson, Susan G. (1995, eds.), Abductive Inference: Computation, Philosophy, Technology, Cambridge University Press, Cambridge, UK.

• Lipton, Peter. (2001). Inference to the Best Explanation, London: Routledge. ISBN 0-415-24202-9.

• Menzies, T. (1996), "Applications of Abduction: Knowledge-Level Modelling, International Journal of Human-Computer Studies, 45.3, 305-335.

• Yu, Chong Ho (1994), "Is There a Logic of Exploratory Data Analysis?", Annual Meeting of American Educational Research Association, New Orleans, LA, April, 1994. :Eprint

Notes

1. ^ Schwendtner, Tibor and Ropolyi, László and Kiss, Olga (eds): Hermeneutika és a természettudományok. Áron Kiadó, Budapest, 2001. It is written in Hungarian. Meaning of the title: Hermeneutics and the natural sciences.
2. ^ Kave Eshghi. Abductive planning with the event calculus. In Robert A. Kowalski, Kenneth A. Bowen editors: Logic Programming, Proceedings of the Fifth International Conference and Symposium, Seattle, Washington, August 15-19, 1988. MIT Press 1988, ISBN 0-262-61056-6
3. ^ April M. S. McMahon (1994): Understanding language change. Cambridge: Cambridge University Press. ISBN 0-521-44665-1

See also

Analogy is both the cognitive process of transferring information from a particular subject (the analogue or source) to another particular subject (the target), and a linguistic expression corresponding to such a process. ... Charles Sanders Peirce (IPA: /pɝs/), (September 10, 1839 – April 19, 1914) was an American polymath, physicist, and philosopher, born in Cambridge, Massachusetts. ... Charles Peirce (Bibliography). ... Deductive reasoning is the kind of reasoning where the conclusion is necessitated or implied by previously known premises. ... Defeasible reasoning (sometimes called defeasible logic) is the study of forms of reasoning that, while convincing, are not as formal and rigorous as deductive reasoning. ... Gregory Bateson (9 May 1904–4 July 1980) was a British anthropologist, social scientist, linguist and cyberneticist whose work intersected that of many other fields. ... Aristotle appears first to establish the mental behaviour of induction as a category of reasoning. ... Wikipedia does not yet have an article with this exact name. ... Logic (from Classical Greek λόγος logos; meaning word, thought, idea, argument, account, reason, or principle) is the study of the principles and criteria of valid inference and demonstration. ... The three methods for logical reasoning, deduction, induction, and abduction can be explained in the following way (taken from [1]): Given α, β, and the rule R1 : α ∴ β Deduction is using the rule and its preconditions to make a conclusion (α ∧ R1 ⇒ β). Induction is learning... An inference procedure is a key component of the knowledge engineering process, sometimes known as abduction. ... A sign relation is the basic construct in the theory of signs, or semiotic theory, as developed by Charles Sanders Peirce (1839-1914). ...

External links

• Josephson, John, "Abductive Inference in Reasoning and Perception", Webpage
• Ryder, Martin, Instructional Technology Connections: Abduction, Webpage
• Magnani, Lorenzo, Abduction, Reason, and Science. Processes of Discovery and Explanation, Webpage
• [it] Magnani, Lorenzo
• Chapter 3. Deduction, Induction, and Abduction in article Charles Sanders Peirce of the Stanford Encyclopedia of Philosophy

This article was originally based on material from the Free On-line Dictionary of Computing, which is licensed under the GFDL. Lorenzo Magnani (born 1952), is an Italian philosopher. ... This article does not cite any references or sources. ... “GFDL” redirects here. ...

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