Conditionals, Counterfactuals, and Rational Reasoning: An Experimental Study on Basic Principles

Pfeifer, Niki; Tulkki, Leena

doi:10.1007/s11023-017-9425-6

Cited by 29 publications

(31 citation statements)

References 58 publications

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“…There is experimental evidence that people judge the probability of a counterfactual, "If A were the case, then C would be the case", as the conditional probability, PpC|Aq [68,78,80]. Moreover, when presented with causal, e.g., "If a patient were to take certain drug, the symptoms would diminish", or non-causal task material, e.g., "If the card were to show a square, it would be black", people judge the negations of the antecedents to be irrelevant to the evaluation of the counterfactuals [78,80]. These negations state the actual facts, e.g., "The patient does not take the drug", or "The side does not show a square", respectively.…”

Section: Two-premise Centering With Logical Relations and Counterfactmentioning

confidence: 99%

Probabilistic inferences from conjoined to iterated conditionals

Sanfilippo

Pfeifer

Over

et al. 2018

International Journal of Approximate Reasoning

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There is wide support in logic, philosophy, and psychology for the hypothesis that the probability of the indicative conditional of natural language, Ppif A then Bq, is the conditional probability of B given A, PpB|Aq. We identify a conditional which is such that Ppif A then Bq " PpB|Aq with de Finetti's conditional event, B|A. An objection to making this identification in the past was that it appeared unclear how to form compounds and iterations of conditional events. In this paper, we illustrate how to overcome this objection with a probabilistic analysis, based on coherence, of these compounds and iterations. We interpret the compounds and iterations as conditional random quantities which, given some logical dependencies, may reduce to conditional events. We show how the inference to B|A from A and B can be extended to compounds and iterations of both conditional events and biconditional events. Moreover, we determine the respective uncertainty propagation rules. Finally, we make some comments on extending our analysis to counterfactuals.

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Section: Two-premise Centering With Logical Relations and Counterfactmentioning

confidence: 99%

Probabilistic inferences from conjoined to iterated conditionals

Sanfilippo

Pfeifer

Over

et al. 2018

International Journal of Approximate Reasoning

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“…Influenced by the above points, psychologists of reasoning have tested the CPH in controlled experiments, and found that people tend to conform to it for a wide range of conditionals, from indicative conditionals ( [31,35,73]) and conditional bets ( [5]) to counterfactuals and causal conditionals ( [69,70,81,82]). In the opinion of some authors, the CPH may not hold for conditionals if A then C when the antecedent A does not raise the probability of the conditional's consequent C ( [26,88]), but the significance of this finding is open to dispute ( [69]), and the general support for the CPH has had a major impact in psychology ( [30,68]), formal epistemology ( [76]), and philosophical logic ( [75,78,79,80]).…”

Section: Introductionmentioning

confidence: 99%

Probabilities of conditionals and previsions of iterated conditionals

Sanfilippo

Gilio

Over

et al. 2020

International Journal of Approximate Reasoning

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We analyze selected iterated conditionals in the framework of conditional random quantities. We point out that it is instructive to examine Lewis's triviality result, which shows the conditions a conditional must satisfy for its probability to be the conditional probability. In our approach, however, we avoid triviality because the import-export principle is invalid. We then analyze an example of reasoning under partial knowledge where, given a conditional if A then C as information, the probability of A should intuitively increase. In our approach, we explain this intuition by making some implicit background information explicit. We consider several (generalized) iterated conditionals, which allow us to formalize different kinds of latent information. We verify that for these iterated conditionals the prevision is greater than or equal to the probability of A. We also investigate the lower and upper bounds of the Affirmation of the Consequent inference. We conclude our study with some remarks on the supposed "independence" of two conditionals, and we interpret this property as uncorrelation between two random quantities.

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“…1 In particular, see the axiomatizations of Renyi (1955) and Popper (1959), and Dubins's extension of de Finetti (1975). A sample of authors endorsing full conditional probabilities includes representatives from philosophy (van Fraassen 1976;Levi 1980;McGee 1994;Hájek 2003;Sprenger and Hartmann 2017), statistics (Kadane, Schervish, and Seidenfeld 1999), economics and game theory (Blume, Brandenburger, and Dekel 1991b;Myerson 1991;Hammond 1994;Battigalli and Veronesi 1996;Kohlberg and Reny 1997), logic (Adams 1966;Coletti and Scozzafava 2002;Makinson 2011), psychology (Pfeifer and Tulkki 2017), and computer science (Kraus, Lehmann, and Magidor 1990;Cowell, Dawid, Lauritzen, and Spiegelhalter 1999;Gilio 2012).…”

Section: Conditional Probability As Primitive: Full Conditional Probabilitiesmentioning

confidence: 99%