‘If’ and the problems of conditional reasoning

@article{Byrne2009IfAT,
  title={‘If’ and the problems of conditional reasoning},
  author={Ruth M. J. Byrne and Philip N. Johnson-Laird},
  journal={Trends in Cognitive Sciences},
  year={2009},
  volume={13},
  pages={282-287}
}

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References

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The Meaning(s) of “If”: Conditional Probabilities and Mental Models
Three experiments with a probabilistic truth-table evaluation task suggest that most people interpret conditionals as asserting a high conditional probability of the consequent, given the antecedent.
Conditionals and directionality: On the meaning of if vs. only if
TLDR
This study uses two types of conditional statement that are logically equivalent: if p then q and p only if q, and reports three experiments that demonstrate the existence of a directional bias in the comprehension of the conditionals.
On the nature of mental models of conditional: The case of If, If then, and Only if
It has recently been reported that forward inferences from if p then q sentences (i.e., from antecedent to consequent) were faster than backward inferences from consequent to antecedent (Barrouillet,
Suppositions, extensionality, and conditionals: a critique of the mental model theory of Johnson-Laird And Byrne (2002).
TLDR
The authors argue that the extensional semantics underlying the Johnson-Laird and Byrne theory is equivalent to that of the material, truth-functional conditional, at least for what they term "basic" conditionals, concerning arbitrary problem content.
The Mental Model Theory of Conditionals: A Reply to Guy Politzer
This paper replies to Politzer’s (2007) criticisms of the mental model theory of conditionals. It argues that the theory provides a correct account of negation of conditionals, that it does not
Reasoning with conditionals
This paper reviews the psychological investigation of reasoning with conditionals, putting an emphasis on recent work. In the first part, a few methodological remarks are presented. In the second
In Search of Counter-Examples: Deductive Rationality in Human Reasoning
TLDR
The results of contextual manipulations that have a bearing on the supposed primacy of System 1 are presented, concur with the thesis in dual-processing frameworks that “Rationality-2 processes” (Evans & Over, 1996), “test procedures’ (Chater & Oaksford, 1999), or “conclusion validation processes“ (Johnson-Laird & Byrne, 1991) serve to override the results of System 2 processes.
Human reasoning includes a mental logic
  • D. O'brien
  • Philosophy
    Behavioral and Brain Sciences
  • 2009
TLDR
Mental-logic theory rejects the use of the material conditional and deals with the completeness problem by limiting the scope of its procedures to local sets of propositions.
Conditionals: A Theory of Meaning, Pragmatics, and Inference
You reason about conditional relations because much of your knowledge is conditional. If you get caught speeding, then you pay a fine. If you have an operation, then you need time to recuperate. If
The negated conditional: a litmus test for the suppositional conditional?
Under the suppositional account of conditionals, when people think about a conditional assertion, "if p then q," they engage in a mental simulation in which they imagine p holds and evaluate the
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