ECAI logo

Workshop report

ECAI'96 Workshop on

Abductive and Inductive Reasoning

Budapest, August 12, 1996

Peter Flach and Antonis Kakas

  1. Introduction
  2. Peirce on abduction and induction
  3. Invited talk: John Josephson
  4. Discussion panel 1: Distinguishing abduction and induction: are they different and how?
  5. Discussion panel 2: Synthesis of abduction and induction: can they be put thogether and how?
  6. Summary of discussions
  7. Concluding remarks
  8. Acknowledgements
  9. Some comments on the report

1. Introduction

This workshop brought together some 20 researchers -- with varying backgrounds in Artificial Intelligence, Machine Learning, Logic Programming and Philosophy -- to discuss the relations and differences between abductive and inductive reasoning as perceived in each of those disciplines. As this workshop was the first in its kind, and also because of the widely different backgrounds of the participants, the main emphasis lay on identifying and clarifying the main issues in the debate, rather than on trying to reach a general consensus on the issues raised. In order to stimulate the exchange of ideas and viewpoints, ample time was devoted to plenary discussions, some of which continued until days after the workshop in impromptu bi- and multilateral meetings.

More specifically, the purpose of the workshop was to address the following two central questions: (i) how are the two forms of reasoning different (if indeed they can be distinguished) and (ii) how can they be integrated together in an Artificial Intelligence enviroment? The workshop was therefore structured around two panel discussions, one on each of these central issues, together with an invited talk for each session. In each of the panel discussions four of the submitted papers were briefly presented by their authors raising problems and questions for the subsequent discussion.

The workshop started with the presentation of the results of an on-line questionnaire which was filled out before arriving at the workshop, as these results provided some insight into the main points of agreement and controversy. The majority of respondents agreed on a definition of induction as inference of general rules from specific observations. Another viewpoint that seemed uncontroversial is that abduction and induction are reasoning forms stemming from a common root. The proper definition of abduction, and its relation with induction, appeared to be more problematic. Roughly two-thirds of the respondents agreed with the definition of abduction as inference to the best explanation, while one-third favours a definition of abduction as hypothesis formation. The main features that distinguish between abduction and induction mentioned by the respondents are: the form of the inferred hypotheses, the utility of the inferred hypotheses, the underlying consequence relations, and the computational methods employed.

2. Peirce on abduction and induction

It was also felt useful to have at the beginning of the workshop a short presentation of abduction and induction as introduced and studied by the American philosopher Charles Sanders Peirce. Consider the Aristotelian syllogism Barbara:
    All the beans from this bag are white. (rule)
    These beans are from this bag. (case)
    Therefore, these beans are white. (result)
By exchanging the result with the rule, one obtains a (deductively invalid) syllogism that can be seen as an inductive generalisation:
    These beans are white. (result)
    These beans are from this bag. (case)
    Therefore, all the beans from this bag are white. (rule)
Alternatively by exchanging the result with the case in Barbara one obtains an abductive syllogism:
    All the beans from this bag are white. (rule)
    These beans are white. (result)
    Therefore, these beans are from this bag. (case)
Here, the conclusion can be seen as an explanation of the result given the rule.

Whereas Peirce's classification of reasoning forms through syllogisms is probably well-known in Artificial Intelligence, it appears to be much less known that Peirce abandoned his syllogistic theory around 1900 in favour of a classification of reasoning forms in terms of the function they perform in science. Three stages are discerned: (1) formulating a hypothesis, (2) drawing predictions from the hypothesis, (3) evaluating these predictions.

The first stage, coming up with an explanatory hypothesis, is what Peirce now calls abduction. Predictions are drawn by deduction; and assessing a hypothesis by evaluating these predictions in the real world is what Peirce calls induction. The whole process is triggered by some surprising observation, and Peirce formulates the following requirement for a hypothesis to be explanatory:

    The surprising fact, C, is observed;
    But if A were true, C would be a matter of course,
    Hence, there is reason to suspect that A is true.
The second condition is usually formalised using deduction, which leads to the following definition of abduction: given a background theory T, A is an abductive explanation of observation C if T together with A deductively entails C.

It should be noted that Peirce's later definition of abduction covers both the second and third syllogism quoted from his early theory, since in both syllogisms the inferred hypothesis entails one of the premisses given the other. One could say that in his later theory Peirce concentrates on the inferential characteristics of abduction (a sort of reversed deduction), while in his early theory he emphasises syllogistic (i.e. syntactical) characteristics.

Some of the workshop participants adhere to the inferential perspective, and therefore view induction as a special case of abduction, while others favour the syllogistic perspective, and therefore stress the differences between abduction and induction. These points formed a central part of the discussion in the panels that followed.

3. Invited talk: John Josephson

The second invited speaker Ryszard Michalski unfortunately was not able to attend the workshop

In his invited talk, John Josephson (Ohio State University) defined abduction as inference to the best explanation or explanatory inference, following a pattern like this:

    D is a collection of data (facts, observations, givens),
    H explains D (would, if true, explain D),
    No other hypothesis explains D as well as H does.
    Therefore, H is probably correct.
By virtue of the third premiss, this pattern provides a justification for concluding H from D. The Artificial Intelligence task is then to define, in a particular context, what it means for H to explain D, and when one explanation is better than another. As for the first question, What is an explanation?, Josephson argued convincingly that this is a matter of causality rather than deductive entailment: some explanations are not deductive proofs, and some deductive proofs are not explanations. We then arrive at a view of abduction as an assignment of causal responsibility, the best way we can.

As for the relation between abduction and induction, it was argued that inductive generalisation is a special case of abduction. The explanation occurs on a metalevel: while the generalisation "all crows are black" does not explain why a particular crow is black, it does explain why we observe a black thing whenever we observe a crow. Furthermore, in induction we are not just interested in any generalisation, but only in the best one(s) (an amusing example of a bad inductive argument is "This thumb is mine; that thumb is mine; therefore, all thumbs are mine").

We thus see that Josephson's position corresponds more or less to Peirce's later theory of abduction as hypothesis formation, but extending it to include hypothesis selection as well.

The slides Josephson used for his presentation can be found at

4. Discussion panel 1: Distinguishing abduction and induction: are they different and how?

Atocha Aliseda (Stanford University, USA) argued that abduction and induction are best perceived as two points in a whole spectrum of explanatory reasoning. Different forms of explanatory reasoning can be obtained by instantiating three parameters: the kind of inference involved in explaining, the kind of observation that needs to be explained, and the kind of explanations (facts, rules theories).

Brigitte Bessant (Universite d'Artois, France) pointed out that we can only increase our insight in abduction and induction if we reach a better understanding of the fundamental concepts on which these reasoning forms are based. Among these fundamental concepts are: the notion of generality between inductive hypotheses, the notion of explanation, and the notion of confirmation (what does it mean for an observation to confirm a hypothesis?).

Marc Denecker (Katholieke Universiteit Leuven, Belgium) argued that syntactical distinctions between abductive hypotheses as ground facts and inductive hypotheses as theories are unsatisfactory. Instead, he proposed a semantic characterisation of the difference between the two by means of possible world models characterisation exploiting a more abstract distinction between general and specific knowledge.

Erich Prem (Austrian Research Institute for AI, Vienna) provided an analysis of the three forms of reasoning from the classical Aristotelian viewpoint, stressing that logic is not so much a "science of truth" or a "science of reasoning", but rather a science of argumentation.

5. Discussion panel 2: Synthesis of abduction and induction: can they be put thogether and how?

John Bell (QMW, University of London, UK) suggested that induction and abduction are both forms of pragmatic, or context-dependent, reasoning. Given a partial epistemic context, induction is the process of expanding the context in the appropriate way and then reasoning deductively, while abduction is the process of expanding the context in the appropriate way such that a purported conclusion can be deduced from it. The notion of pragmatic entailment can be used to provide a common model-theoretic framework for induction and abduction.

Nicolas Lachiche (INRIA, France) presented a formal separation of abduction and induction by relating each one to a different form of completion of the given background knowledge base. This distinction though is confined only to the specific case of confirmatory induction.

Stathis Psillos (London School of Economics, UK) proposed a set of desiderata that a general model of ampliative reasoning from incomplete information should satisfy. As Josephson, Psillos argued that abduction understood as inference to the best explanation best satisfies these desiderata, encompassing inductive generalization as a special case.

Fabrizio Riguzzi (Universita di Bologna, Italy) presented a framework in which it is possible to integrate abduction and induction as these are used in the context of Logic Programming. This can increase the learning capabilities of Inductive Logic Programming, as it allows a system to learn abductive logic programs from background programs with integrity constraints.

6. Summary of discussions

It was clear from the beginning that there would be many different opinions on the issues addressed among the participants. Furthermore, it transpired that it was not easy to agree, at the current stage of the debate, on the list of the particular problems and issues that should form the central points of investigation in the overall task of analysing the relation between abduction and induction. Two main schools of thought emerged. In the first the emphasis is put on unifying the two into a common form (identifying one as a special case of the other) while in the second the emphasis is on clearly separating the two by identifying their main characteristics. Hence the need to have two conceptually different forms of ampliative reasoning from incomplete information was put under question.

On the other hand, if two such forms should exist we need to clarify the differences in their operation and also the difference in the tasks that they can achieve. One difference that most people seemed to agree upon is that abduction presupposes a general theory about the domain of interest. The abductive explanations or conclusions are understood relative to this theory. Furthermore, it emerged that the utility for each form (and the subsequent computational model) may be an important distinguishing indicator of the two. While it was argued that the two can be conceptually unified under abduction (itself interpreted as inference to the best explanation) using a meta-theory of sampling as the "causal" theory for induction, it was pointed out that problems in AI seem to need two quite distinct forms of reasoning for different tasks employing different computational models.

In this AI (perhaps extreme) view we should not expect that there are Platonic ideals of abduction and induction that we are trying to capture but rather that abduction and induction are simply processes that are needed for solving practical problems. However, the discussions at this workshop seemed to suggest that many people do try to capture Platonic ideals, but that these ideals differ among different people. In particular, some of the work presented in the workshop has provided a possible first step towards such a Platonic separation of the two using possible world semantics to formalise their differences. If indeed there are many such alternative proposals, then the first and perhaps most important step is to disentangle these different ideals, and to distinguish them terminologically. Only then can we hope to formalise them in a satisfying manner.

7. Concluding remarks

Perhaps the main result of this workshop was to bring to the fore, and make people aware of, the different perspectives on abduction and induction. The continued discussions between the participants on the days that followed, well after the workshop had ended, indicate the useful role that it has played in putting together these ideas. We feel that we are now in a better position to formulate the main issues that need to be addressed before we can develop a coherent account of abduction and induction. The short time available did not allow ample discussion around the second central question of "how can abduction and induction be integrated together in an Artificial Intelligence environment" which in fact was overshadowed by the first issue of the comparison and distinction of the two forms of reasoning. This issue of integration will be taken up at a follow-up workshop.

In the meantime, an electronic mailing list has been established for continuation of the discussions started at the workshop. Those interested in participating in this mailing list should send an email to

The workshop notes contain 15 short papers and are available on-line through the workshop's WWW-pages at; a limited number of hardcopies is still available from Marc Denecker (email:


This workshop has been made possible by financial support from the European Networks of Excellence CompulogNet (Computational Logic) and MLnet (Machine Learning). Writing of this report has been partially supported by the Esprit Long Term Research Project 20237 (Inductive Logic Programming 2).
After distributing a first draft we have received some interesting comments from
Last change: January 30, 1997 / Peter Flach