Abstract
Since the 1970s Peirce’s notion of abduction has become an inspiration for many scholars in formal logic and Artificial Intelligence. This chapter outlines some examples of logical approaches to abductive reasoning. Abduction can be formulated as a rule of inference, which leads to “adaptive logics” of discovery in the family of paraconsistent logics, Abductive Logic Programming, and to non-propositional model-based reasoning (Sect. 3.1). Analysis of the notion of explanation helps to characterize structural rules for abduction (Sect. 3.2). Atocha Aliseda treats the abductive search of missing explanatory premises by means of Beth’s semantic tableaux (Sect. 3.3). The GW-model of Dov Gabbay and John Woods argues that abduction is subjunctive and ignorance-preserving (Sect. 3.4). In Jaakko Hintikka’s interrogative model of inquiry abduction plays an important role in strategic truth-seeking by questioning (Sect. 3.5).
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Notes
- 1.
Peirce himself made this suggestion in 1868 by stating that every deductive syllogism may be put into the form MP, so that hypothetic inference may be called “reasoning from consequent to antecedent” (W 2:219–220; EP 1:35).
- 2.
- 3.
Fisher’s statistical significance tests were based on probabilistic Modus Tollens, i.e. the null hypothesis H is rejected if the data is very improbable given H, but Neyman and Pearson replaced such tests with comparisons of the likelihoods of rival hypotheses.
- 4.
For a survey of paraconsistent logics and their connection to abduction, see Bueno-Soler et al. (2017) .
- 5.
Meheus and Batens (2006) call, in a somewhat peculiar way, adaptive logics with the rule (6) “practical abduction”, while “theoretical abduction ” allows the derivation of the disjuncts at least as possibilities.
- 6.
For a system of causal abduction, where the arrow → is taken from the conditional logic of Chellas, see Beirlaen and Aliseda (2014). This framework avoids abductive conclusions which are self-explanations, contradictory explanations or overinformative explanations.
- 7.
- 8.
Nepomuceno-Fernández and Soler-Toscano (2007) define a relation of converse explanation A € B by the condition that B entails all elements of A, and give structural rules for €. In contrast to our irreflexivity (15), they accept self-explanations and thus allow reflexivity.
- 9.
The first application of the tableaux method to abduction was given by Mayer and Pirri (1993).
- 10.
- 11.
In a fair lottery, the probability that a given single ticket wins is low, even though it is not surprising that at least one among many voters wins.
- 12.
For how possible explanations in the theory of evolution, see Sect. 4.4.
- 13.
For a survey, see Niiniluoto (2011c).
- 14.
The idea that experiments are questions to nature goes back to Francis Bacon and Kant (see Sintonen 2009) .
- 15.
The reviewer of this book points out that the distinction between definitory and strategic rules corresponds to the fourteenth century philosopher William Burley’s distinction between rules that “constitute the practice” and the rules that “pertain to its being practiced well”.
- 16.
Hamami (2015) extends Hintikka’s model to a multi-agent setting, which has been studied in dynamic epistemic logic .
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Niiniluoto, I. (2018). Abduction and Logic. In: Truth-Seeking by Abduction. Synthese Library, vol 400. Springer, Cham. https://doi.org/10.1007/978-3-319-99157-3_3
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