, Experiment 8: Coherence interval width and response confidence 7.1.1 Varying location and width of coherence intervals 7.1.2 Measuring people's sensitivity to location and width

E. W. Adams, The Logic of Conditionals, 1975.

E. Adams, Four probability-preserving properties of inferences, Journal of Philosophical Logic, issue.1, pp.1-24, 1996.

E. Adams, A primer of probability logic, 1998.

L. G. Allan, A note on the measurement of contingency between two binary variables in judgment tasks, Bulletin of the Psychometric Society, vol.15, pp.147-149, 1980.

N. Ali, N. Chater, and M. Oaksford, The mental representation of causal conditional reasoning: Mental models or causal models, Cognition, vol.119, pp.403-418, 2011.

A. Appiah, Jackson on the material conditional, Australasian journal of Philosophy, vol.62, pp.77-81, 1984.

R. H. Baayen, D. J. Davidson, and D. M. Bates, Mixed effects modeling with crossed random effects for subjects and items, Journal of Memory and Language, vol.59, pp.390-412, 2008.

J. Baratgin, I. Douven, J. Evans, . B. St, M. Oaksford et al., The new paradigm and mental models, Trends in Cognitive Sciences, vol.19, issue.10, pp.547-548, 2015.

J. Baratgin, D. E. Over, and G. Politzer, Uncertainty and the de Finetti tables, Thinking & Reasoning, vol.19, pp.308-328, 2013.
URL : https://hal.archives-ouvertes.fr/ijn_01295433

J. Baratgin and G. Politzer, Updating: A psychologically basic situation of probability revision, Thinking & Reasoning, vol.16, pp.245-287, 2010.
URL : https://hal.archives-ouvertes.fr/ijn_00512278

J. Baratgin and G. Politzer, Logic, probability, and inference: A methodology for a new paradigm, Cognitive Unconscious and Human Rationality, 2016.

M. Bar-hillel and E. Neter, How alike is it versus how likely is it: A disjunction fallacy in probability judgments, Journal of Personality and Social Psychology, vol.65, issue.6, pp.1119-1131, 1993.

D. J. Barr, Random effects structure for testing interactions in linear mixed-effects models, Frontiers in Psychology, vol.4, p.328, 2013.

D. J. Barr, R. Levy, C. Scheepers, and H. J. Tily, Random effects structure for confirmatory hypothesis testing: Keep it maximal, Journal of Memory and Language, vol.68, pp.255-278, 2013.

P. Barrouillet and C. Gauffroy, Probability in reasoning: A developmental test on conditionals, Cognition, vol.137, pp.22-39, 2015.

P. Barrouillet, C. Gauffroy, and J. Lecas, Mental models and the suppositional account of conditionals, Psychological Review, vol.115, issue.3, pp.760-772, 2008.

P. Barrouillet, N. Grosset, and J. Lecas, Conditional reasoning by mental models: Chronometric and developmental evidence, Cognition, vol.75, pp.237-266, 2000.

P. Barrouillet and J. Lecas, Mental models in conditional reasoning and working memory, Thinking and Reasoning, vol.5, issue.4, pp.289-302, 1999.

D. Bates, R. Kliegl, S. Vasishth, and H. Baayen, Parsimonious mixed models, 2015.

J. Bennett, A philosophical guide to conditionals, 2003.

N. Bonini, K. Tentori, and D. Osherson, A different conjunction fallacy. Mind and Language, vol.19, pp.199-210, 2004.

J. Bonnefon, New ambitions for a new paradigm: Putting the psychology of reasoning at the service of humanity, Thinking & Reasoning, vol.19, issue.3, pp.381-398, 2013.

R. Bradley, Multidimensional possible-world semantics for conditionals, Philosophical Review, vol.121, issue.4, pp.539-571, 2012.

M. D. Braine and &. O'brien, Mental logic, 1998.

M. D. Braine, B. J. Reiser, and B. Rumain, Some empirical justification for a theory of natural propositional logic, Psychology of Learning and Motivation, vol.18, pp.313-337, 1984.

R. B. Braithwaite, Scientific Explanation, 1953.

N. R. Bramley, P. Dayan, T. L. Griffiths, and D. A. Lagnado, Formalizing Neurath's ship: Approximate algorithms for online causal learning, Psychological Review, vol.124, issue.3, pp.301-338, 2017.

M. Bucciarelli and P. N. Johnson-laird, Strategies in syllogistic reasoning, Cognitive Science, vol.23, issue.3, pp.247-303, 1999.

R. M. Byrne, Suppressing valid inferences with conditionals, Cognition, vol.31, pp.61-83, 1989.

R. M. Byrne, Counterfactual thought, Annual Review of Psychology, vol.67, pp.135-157, 2016.

R. M. Byrne and P. N. Johnson-laird, If' and the problems of conditional reasoning, Trends in Cognitive Sciences, vol.13, issue.7, pp.282-287, 2009.

R. M. Byrne and P. N. Johnson-laird, Conditionals and possibilities, 2010.

, Cognition and conditionals: Probability and logic in human thought, pp.55-68

A. Capotorti, L. Galli, and B. Vantaggi, How to use locally strong coherence in an inferential process based on upper-lower probabilities, Soft Computing, vol.7, issue.5, pp.280-287, 2003.

F. Cariani and L. J. Rips, Conditionals, context, and the suppression effect, Cognitive Science, vol.41, issue.3, pp.540-589, 2017.

R. Carnap, The logical Foundations of Probability (2 nd, 1950.

N. Chater and C. D. Manning, Probabilistic models of language processing and acquisistion, Trends in Cognitive Sciences, vol.7, pp.335-344, 2006.

N. Chater and M. Oaksford, The probability heuristics model of syllogistic reasoning, Cognitive Psychology, vol.38, pp.191-258, 1999.

N. Chater and M. Oaksford, Normative systems: Logic, probability, and rational choice, The Oxford handbook of thinking and reasoning, pp.11-21, 2012.

N. Chater and M. Oaksford, Programs as causal models: Speculations on mental programs and mental representation, Cognitive Science, vol.37, pp.1171-1191, 2013.

N. Chater, M. Oaksford, U. Hahn, and E. Heit, Bayesian models of cognition, Wiley Interdisciplinary Reviews: Cognitive Science, vol.1, issue.6, pp.811-823, 2010.

P. W. Cheng, From covariation to causation: A causal power theory, Psychological Review, vol.104, issue.2, pp.367-405, 1997.

G. Coletti and R. Scozzafava, Probabilistic logic in a coherent setting, 2002.

L. Cosmides and J. Tooby, Are humans good intuitive statisticians after all? Rethinking some conclusions from the literature on judgment under uncertainty, Cognition, vol.58, issue.1, pp.1-73, 1996.

F. Costello and P. Watts, Surprisingly rational: Probability theory plus noise explains biases in judgment, Psychological Review, vol.121, issue.3, pp.463-480, 2014.

F. Costello and P. Watts, People's conditional probability judgments follow probability theory (plus noise), Cognitive Psychology, vol.89, pp.106-133, 2016.

F. Costello and P. Watts, A test of two models of probability judgment: Quantum versus noisy probability, Proceedings of the 38 th Annual Conference of the Cognitive Science Society, pp.1104-1109, 2016.

F. Costello and P. Watts, Mathematical invariants in people's probabilistic reasoning, The 39th Annual Meeting of the Cognitive Science Society, 2017.

V. Crupi, B. Fitelson, and K. Tentori, Probability, confirmation, and the conjunction fallacy, Thinking & Reasoning, vol.14, issue.2, pp.182-199, 2008.

V. Crupi, K. Tentori, and L. Lombardi, Pseudodiagnosticity revisited, Psychological Review, vol.116, issue.4, pp.971-985, 2009.

N. Cruz, J. Baratgin, M. Oaksford, and D. E. Over, Bayesian reasoning with ifs and ands and ors, Frontiers in Psychology, vol.6, p.192, 2015.

N. Cruz and K. Oberauer, Comparing the meanings of "if" and "all, Memory & Cognition, vol.42, pp.1345-1356, 2014.

N. Cruz, D. Over, and M. Oaksford, The elusive oddness of or-introduction, The 39th Annual Meeting of the Cognitive Science Society, pp.259-264, 2017.

N. Cruz, D. Over, M. Oaksford, and J. Baratgin, Centering and the meaning of conditionals, Proceedings of the 38th Annual Conference of the Cognitive Science Society, pp.1104-1109, 2016.

G. Cumming and S. Finch, Inference by eye: Confidence intervals and how to read pictures of data, American Psychologist, vol.60, issue.2, pp.170-180, 2005.

D. D. Cummins, Naive theories and causal deduction, Memory & Cognition, vol.23, issue.5, pp.646-658, 1995.

D. D. Cummins, T. Lubart, O. Alksnis, and R. Rist, Conditional reasoning and causation, Memory & Cognition, vol.19, issue.3, pp.274-282, 1991.

B. De-finetti, /1995): The logic of probability, Philosophical Studies, vol.77, pp.181-190, 1936.

D. Edgington, Counterfactuals. The Presidential Address, Proceedings of the Aristotelian Society, CVIII, issue.1, pp.1-21, 2008.

D. Edgington, Causation first: Why causation is prior to counterfactuals, 2011.

D. Edgington, The Stanford Encyclopedia of Philosophy, 2014.

S. Elqayam, Scams and rationality: Dutch book arguments are not all they're cracked up to be, 2016.

S. Elqayam and D. E. Over, New paradigm psychology of reasoning: An introduction to the special issue edited by S. Elqayam, J.F. Bonnefon, & D. E. Over. Thinking & Reasoning, vol.19, pp.249-265, 2013.

S. Elqayam and D. Over, Editorial: From is to ought: The place of normative models in the study of human thought, Frontiers in Psychology, vol.7, p.628, 2016.

O. Espino and R. M. Byrne, The compatibility heuristic in non-categorical hypothetical reasoning: Inferences between conditionals and disjunctions, Cognitive Psychology, vol.67, pp.98-129, 2013.

J. Evans and . B. St, Interpretation and matching bias in a reasoning task, Quarterly Journal of Experimental Psychology, vol.24, pp.193-199, 1972.

J. Evans and . B. St, In two minds: Dual-process accounts of reasoning, Trends in Cognitive Sciences, vol.7, issue.10, pp.454-459, 2003.

J. Evans and . B. St, The heuristic-analytic theory of reasoning: Extension and evaluation, Psychonomic Bulletin & Review, vol.13, issue.3, pp.378-395, 2006.

J. Evans and . B. St, On the resolution of conflict in dual-process theories of reasoning, Thinking & Reasoning, vol.13, issue.4, pp.321-339, 2007.

J. Evans and . B. St, Dual-processing accounts of reasoning, judgment, and social cognition, Annual Review of Psychology, vol.59, pp.255-278, 2008.

J. Evans and . B. St, Intuition and reasoning: A dual-process perspective, Psychological Inquiry, vol.21, pp.313-326, 2010.

J. Evans and . B. St, Questions and challenges for the new psychology of reasoning, Thinking & Reasoning, vol.18, issue.1, pp.5-31, 2012.

J. Evans and . B. St, Dual process theory: Perspectives and problems, Dual Process Theory 2.0, 2017.

J. Evans, . B. St, J. Clibbens, and B. Rood, Bias in conditional inference: Implications for mental models and mental logic, The Quarterly Journal of Experimental Psychology, vol.48, issue.3, pp.644-670, 1995.

J. Evans, . B. St, and S. J. Handley, The role of negation in conditional inference, The Quarterly Journal of Experimental Psychology, vol.52, issue.3, pp.739-769, 1999.

J. Evans, . B. St, S. J. Handley, and A. M. Bacon, Reasoning under time pressure: A study of causal conditional inference, Experimental Psychology, vol.56, issue.2, pp.77-83, 2009.

J. Evans, . B. St, S. J. Handley, C. Hadjichristidis, V. Thompson et al., On the basis of belief in causal and diagnostic conditionals, The Quarterly Journal of Experimental Psychology, issue.5, pp.635-643, 2007.

J. Evans, . B. St, S. Handley, H. Neilens, and D. E. Over, Thinking about conditionals: A study of individual differences, Memory & Cognition, vol.35, pp.1772-1784, 2007.

J. Evans, . B. St, S. J. Handley, H. Neilens, and D. Over, The influence of cognitive ability and instructional set on causal conditional inference, The Quarterly Journal of Experimental Psychology, vol.63, issue.5, pp.892-909, 2010.

J. Evans, . B. St, S. J. Handley, and D. E. Over, Conditionals and conditional probability, Journal of Experimental Psychology: Learning, Memory, and Cognition, vol.29, pp.321-335, 2003.

J. Evans, . B. St, S. J. Handley, N. Perham, D. E. Over et al., , 2000.

, Frequency versus probability formats in statistical word problems, Cognition, vol.77, pp.197-213

J. Evans, . B. St, and D. E. Over, , 2004.

J. Evans, . B. St, and D. E. Over, Reasoning to and from belief: Deduction and induction are still distinct, Thinking & Reasoning, vol.19, pp.268-283, 2013.

J. Evans, . B. St, D. E. Over, and S. J. Handley, Suppositions, extensionality, and conditionals: A critique of the mental model theory of, 2002.

, Psychological Review, vol.112, issue.4, pp.1040-1052

J. Evans, . B. St, D. E. Over, and K. I. Manktelow, Reasoning, decision making, and rationality, Cognition, vol.49, pp.165-187, 1993.

J. Evans, . B. St, and K. Stanovich, Dual-process theories of higher cognition: Advancing the debate, Perspectives on Psychological Science, vol.8, issue.3, pp.223-241, 2013.

J. Evans, . B. St, V. Thompson, and D. E. Over, Uncertain deduction and conditional reasoning, Frontiers in Psychology, vol.6, p.398, 2015.

P. M. Fernbach, A. Darlow, and S. A. Sloman, Neglect of alternative causes in predictive but not diagnostic reasoning, Psychological Science, vol.21, issue.3, pp.329-336, 2010.

J. Fiser, P. Berkes, G. Orbán, and M. Lengyel, Statistically optimal perception and learning: from behavior to neural representations, Trends in Cognitive Sciences, vol.14, pp.119-130, 2010.

R. A. Fisher, Statistical Methods and Scientific Inference, 1956.

S. Franssens and W. De-neys, The effortless nature of conflict detection during thinking, Thinking & Reasoning, vol.15, issue.2, pp.105-128, 2009.

A. J. Fugard, N. Pfeifer, and B. Mayerhofer, Probabilistic theories of reasoning need pragmatics too: Modulating relevance in uncertain conditionals, Journal of Pragmatics, vol.43, pp.2034-2042, 2011.

A. J. Fugard, N. Pfeifer, B. Mayerhofer, and G. D. Kleiter, How people interpret conditionals: Shifts toward the conditional event, Journal of Experimental Psychology: Learning, Memory, and Cognition, vol.37, pp.635-648, 2011.

S. M. Geiger and K. Oberauer, Reasoning with conditionals: Does every counterexample count? It's frequency that counts, Memory & Cognition, vol.35, issue.8, pp.2060-2074, 2007.

S. M. Geiger and K. Oberauer, Towards a reconciliation of mental model theory and probabilistic theories of conditionals, Cognition and conditionals: Probability and logic in human thinking, pp.289-308, 2010.

C. George, Reasoning from uncertain premises. Thinking and Reasoning, vol.3, pp.161-190, 1997.

G. Gigerenzer and U. Hoffrage, How to improve Bayesian reasoning without instruction: Frequency formats, Psychological Review, vol.102, issue.4, pp.684-704, 1995.

A. Gilio, Criterio di penalizzazione e condizioni di coerenza nella valutazione soggettiva della probabilità. Bollettino dell'Unione Matematica Italiana, vol.7, pp.645-660, 1990.

A. Gilio, Probabilistic reasoning under coherence in System P, Annals of Mathematics and Artificial Intelligence, vol.34, pp.5-34, 2002.

A. Gilio and D. E. Over, The psychology of inferring conditionals from disjunctions: A probabilistic study, Journal of Mathematical Psychology, vol.56, pp.118-131, 2012.

A. Gilio, D. E. Over, N. Pfeifer, and G. Sanfilippo, Centering and compound conditionals under coherence, 2016.

M. A. Gagolewski, P. Gil, and . Grzegorzewski, Soft methods for data science, pp.253-260

A. Gilio and G. Sanfilippo, Conditional random quantities and compounds of conditionals, Studia Logica, vol.102, issue.4, pp.709-729, 2014.

V. Girotto and P. N. Johnson-laird, The probability of conditionals, Psychologia, vol.47, pp.207-225, 2004.

V. Girotto and P. N. Johnson-laird, Conditionals and probability, Cognition and conditionals: Probability and logic in human thinking, pp.103-116, 2010.

V. Goel, Anatomy of deductive reasoning, Trends in Cognitive Sciences, vol.11, issue.10, pp.435-441, 2007.

V. Goel, Cognitive neuroscience of thinking, Handbook of Neuroscience for the Behavioral Sciences, I, pp.417-430, 2009.

G. P. Goodwin, Is the basic conditional probabilistic, Journal of Experimental Psychology: General, vol.143, pp.1214-1241, 2014.

H. P. Grice, Studies in the way of words, 1989.

T. L. Griffiths and J. B. Tenenbaum, Theory-based causal induction, Psychological Review, vol.116, issue.4, pp.661-716, 2009.

C. Hadjichristidis, S. A. Sloman, and D. E. Over, Categorical induction from uncertain premises: Jeffrey's doesn't completely rule, Thinking & Reasoning, vol.20, issue.4, pp.405-431, 2014.

U. Hahn, The Bayesian boom: good thing or bad?, Frontiers in Psychology, vol.5, p.765, 2014.

U. Hahn, A. J. Harris, and A. Corner, Public perception of climate science: Coherence, reliability, and independence, Topics in Cognitive Science, vol.8, pp.180-195, 2016.

U. Hahn and M. Oaksford, The rationality of informal argumentation: A Bayesian approach to reasoning fallacies, Psychological Review, vol.114, pp.646-678, 2007.

A. Hájek, The Stanford Encyclopedia of Philosophy, 2012.

S. J. Handley, S. E. Newstead, and D. Trippas, Logic, beliefs, and instruction: A test of the default interventionist account of belief bias, Journal of Experimental Psychology: Learning, Memory, and Cognition, vol.37, issue.1, pp.28-43, 2011.

S. J. Handley and D. Trippas, Dual processes and the interplay between knowledge and structure: A new parallel processing model, Psychology of Learning and Motivation, vol.62, pp.33-58, 2015.

S. Hartmann and S. Rafiee-rad, Learning conditionals, 2014.

M. Hattori, Probabilistic representation in syllogistic reasoning: A theory to integrate mental models and heuristics, Cognition, vol.157, pp.296-320, 2016.

C. G. Hempel, Studies in the logic of confirmation. Mind, vol.54, pp.97-121, 1945.

. Hintikka, On a Combined System of Inductive Logic. Studia Logico-Mathematica et Philosophica in Honorem Rolf Nevanlinna, Acta Philosophica Phennica, vol.18, pp.21-30, 1965.

C. Howson and P. Urbach, Scientific reasoning: The Bayesian approach (3 rd Ed.), 2006.

J. J. Hox, M. Moerbeek, . Van-de, and R. Schoot, Multilevel analysis: Techniques and applications, 2018.

A. S. Hsu, N. Chater, and P. M. Vitányi, The probabilistic analysis of language acquisition: theoretical, computational, and experimental analysis, Cognition, vol.120, pp.380-390, 2011.

F. Jackson, Conditionals, 1987.

R. C. Jeffrey, If (abstract), Journal of Philosophy, vol.61, pp.702-703, 1964.

R. C. Jeffrey, The Logic of Decision (2 nd Ed, 1990.

R. C. Jeffrey, Matter of fact conditionals, Proceedings of the Aristotelian Society, Supplementary Volumes, vol.65, pp.161-183, 1991.

P. N. Johnson-laird and R. M. Byrne, , 1991.

P. N. Johnson-laird, Mental models and probabilistic thinking, Cognition, vol.50, pp.189-209, 1994.

P. N. Johnson-laird and R. M. Byrne, Conditionals: A theory of meaning, pragmatics, and inference, Psychological Review, vol.109, issue.4, pp.646-678, 2002.

P. N. Johnson-laird, S. Khemlani, and G. P. Goodwin, Logic, probability, and human reasoning, Trends in Cognitive Sciences, vol.19, issue.4, pp.201-214, 2015.

P. N. Johnson-laird, P. Legrenzi, V. Girotto, M. S. Legrenzi, and J. P. Caverni, Naive probability: A mental model theory of extensional reasoning, Psychological Review, vol.106, pp.62-88, 1999.

P. N. Johnson-laird and M. Ragni, What are the possibilities, The 10 th London Reasoning Workshop, 2017.

P. N. Johnson-laird and F. Savary, Illusory inferences: A novel class of erroneous deductions, Cognition, vol.71, pp.191-229, 1999.

P. N. Johnson-laird and J. Tagart, How implication is understood, The American Journal of Psychology, vol.82, issue.3, pp.367-373, 1969.

C. M. Judd, J. Westfall, and D. A. Kenny, Treating stimuli as a random factor in social psychology: A new and comprehensive solution to a pervasive but largely ignored problem, Journal of Personality and Social Psychology, vol.103, issue.1, pp.54-69, 2012.

P. Juslin, H. Nilsson, and A. Winman, Probability theory, not the very guide of life, Psychological Review, vol.116, pp.856-874, 2009.

D. Kahneman and A. Tversky, Prospect theory: An analysis of decision under risk, Econometrica, vol.47, issue.2, pp.263-292, 1979.

I. Kant, Kritik der Reinen Vernunft, 1781.

D. Kellen, H. Singmann, and W. H. Batchelder, Classic-probability accounts of mirrored (Quantum-like) order effects in human judgments, 2017.

J. Kemeny, Fair bets and inductive probabilities, Journal of Symbolic Logic, vol.20, issue.3, pp.263-273, 1955.

D. Kersten and A. Yuille, Bayesian models of object perception, Current Opinion in Neurobiology, vol.13, pp.150-158, 2003.

J. M. Keynes, A treatise on Probability, 1921.

S. S. Khemlani, A. K. Barbey, and P. N. Johnson-laird, Causal reasoning with mental models, Frontiers in Human Neuroscience, vol.8, p.849, 2014.

S. S. Khemlani, T. Hinterecker, and P. N. Johnson-laird, The provenance of modal inference, 2017.

, Annual Meeting of the Cognitive Science Society

S. S. Khemlani, M. Lotstein, and P. N. Johnson-laird, Naive probability: Model-based estimates of unique events, Cognitive Science, vol.39, issue.6, pp.1216-1258, 2015.

K. C. Klauer, S. Beller, and M. Hütter, Conditional reasoning in context: A dual-source model of probabilistic inference, Journal of Experimental Psychology: Learning, Memory, and Cognition, vol.36, issue.2, pp.298-323, 2010.

J. Klayman, . Ha, and . Young-won, Confirmation, disconfirmation, and information in hypothesis testing, Psychological Review, vol.94, issue.2, pp.211-228, 1987.

W. Kneale and M. Kneale, The development of logic, 1962.

A. N. Kolmogorov, Foundations of the theory of probability, 1933.

S. Kripke, Semantical analysis of modal logics, I. Zeitschrift für, Mathematische Logik und Grundlagen der Mathematik, vol.9, pp.67-96, 1963.

K. Krzy?anowska, S. Wenmackers, and I. Douven, Inferential conditionals and evidentiality, Journal of Logic, Language and Information, vol.22, issue.3, pp.315-334, 2013.

H. E. Kyburg and H. E. Smokler, Introduction, Studies in Subjective Probability, pp.1-22, 1980.

D. A. Lagnado and T. Gerstenberg, Causation in legal and moral reasoning, pp.565-601, 2017.

R. S. Lehman, On confirmation and rational betting, Journal of Symbolic Logic, vol.20, issue.3, pp.251-262, 1955.

D. J. Leiner, SoSci Survey (Version 2.5.00-i) [Computer software, 2014.

D. Lewis, Counterfactuals, 1973.

D. Lewis, Probabilities of conditionals and conditional probabilities, Philosophical Review, vol.85, pp.297-315, 1976.

I. Liu, K. Lo, and J. Wu, A probabilistic interpretation of "if-then, Quarterly Journal of Experimental Psychology, vol.49, pp.828-844, 1996.

G. Malinas and J. Bigelow, The Stanford Encyclopedia of Philosophy, 2016.

K. I. Manktelow and D. E. Over, Social roles and utilities in reasoning with deontic conditionals, Cognition, vol.39, pp.85-105, 1991.

H. Markovits and P. Barrouillet, The development of conditional reasoning: A mental model account, Developmental Review, vol.22, pp.5-36, 2002.

H. Markovits, J. Brisson, and P. Chantal, Additional evidence for a dual-strategy model of reasoning: Probabilistic reasoning is more invariant than reasoning about logical validity, Memory & Cognition, vol.43, pp.1208-1215, 2015.

H. Markovits, M. Brunet, V. Thompson, and J. Brisson, Direct evidence for a dualprocess model of deductive inference, Journal of Experimental Psychology: Learning, Memory, and Cognition, vol.39, issue.4, pp.1213-1222, 2013.

H. Markovits, H. Lortie-forgues, and M. Brunet, Conditional reasoning, frequency of counterexamples, and the effect of response modality, Memory & Cognition, vol.38, issue.4, pp.485-492, 2010.

D. Marr, Vision: A computational investigation into the human representation and processing of visual information, 1982.

M. E. Masson and G. R. Loftus, Using confidence intervals for graphically based data interpretation, Canadian Journal of Experimental Psychology, vol.57, issue.3, pp.203-220, 2003.

V. Mcgee, A counterexample to modus ponens, The Journal of Philosophy, vol.82, issue.9, pp.462-471, 1985.

J. B. Misyak and N. Chater, Virtual bargaining: A theory of social decision-making, Philosophical transactions of the Royal Society B, vol.369, pp.1-9, 2014.

S. Nakagawa and H. Schielzeth, A general and simple method for obtaining R 2 for generalized linear mixed-effects models, Methods in Ecology and Evolution, vol.4, pp.133-142, 2013.

J. Neyman, Lectures and Conferences on mathematical Statistics and Probability (2 nd, 1952.

M. Oaksford, Contrast classes and matching bias as explanations of the effects of negation on conditional reasoning, Thinking and Reasoning, vol.8, issue.2, pp.135-151, 2002.

M. Oaksford, Quantum probability, intuition, and human rationality, Behavioral and Brain Sciences, vol.36, p.303, 2013.

M. Oaksford, Imaging deductive reasoning and the new paradigm, Frontiers in Human Neuroscience, vol.9, p.101, 2015.

M. Oaksford and N. Chater, Rational explanation of the Selection task, Psychological Review, vol.103, issue.2, pp.381-391, 1996.

M. Oaksford and N. Chater, The probabilistic approach to human reasoning, Trends in Cognitive Sciences, vol.5, issue.8, pp.349-357, 2001.

M. Oaksford and N. Chater, Optimal data selection: Revision, review, and reevaluation, Psychonomic Bulletin & Review, vol.10, issue.2, pp.289-318, 2003.

M. Oaksford and N. Chater, Bayesian rationality: The probabilistic approach to human reasoning, 2007.

M. Oaksford and N. Chater, Causation and conditionals in the cognitive science of human reasoning, The Open Psychology Journal, vol.3, pp.105-118, 2010.

M. Oaksford and N. Chater, Conditionals and constraint satisfaction: Reconciling mental models and the probabilistic approach, Cognition and Conditionals: Probability and logic in human thought, pp.309-334, 2010.

U. K. Oxford,

M. Oaksford and N. Chater, Dual systems and dual processes but a single function, pp.339-352, 2011.

M. Oaksford and N. Chater, Dual processes, probabilities, and cognitive architecture, Mind & Society, vol.11, pp.15-26, 2012.

M. Oaksford and N. Chater, Dynamic inference and everyday conditional reasoning in the new paradigm, Thinking & Reasoning, vol.19, pp.346-379, 2013.

M. Oaksford and N. Chater, Probabilities, causation, and logic programming in conditional reasoning: Reply to Stenning and van Lambalgen, Thinking & Reasoning, vol.22, issue.3, pp.355-368, 2016.

M. Oaksford and N. Chater, Causal models and conditional reasoning, 2017.

M. Oaksford, N. Chater, and J. Larkin, Probabilities and polarity biases in conditional inference, Journal of Experimental Psychology: Learning, Memory, and Cognition, vol.26, issue.4, pp.883-899, 2000.

M. Oaksford and S. Hall, On the source of human irrationality, Trends in Cognitive Sciences, vol.20, issue.5, pp.336-344, 2016.

M. Oaksford, D. Over, and N. Cruz, Paradigms, possibilities, and probabilities: Comment on Hinterecker et, 2016.

M. Oaksford and K. Stenning, Reasoning with conditionals containing negated constituents, Journal of Experimental Psychology: Learning, Memory, and Cognition, vol.18, issue.4, pp.835-854, 1992.

K. Oberauer, Reasoning with conditionals: A test of formal models of four theories, Cognitive Psychology, vol.53, pp.238-283, 2006.

K. Oberauer, The focus of attention in working memory -from metaphors to mechanisms, Frontiers in Human Neuroscience, vol.7, p.673, 2013.

K. Oberauer, S. Geiger, and K. Fischer, Conditionals and disjunctions, 2010.

, The Science of Reason: A festschrift for, pp.93-118

K. Oberauer, S. M. Geiger, and K. Fischer, Conditionals and disjunctions, 2011.

, The Science of Reason, pp.93-118

K. Oberauer, S. M. Geiger, K. Fischer, and A. Weidenfeld, Two meanings of "if"? Individual differences in the interpretation of conditionals, The Quarterly Journal of Experimental Psychology, vol.60, issue.6, pp.790-819, 2007.

K. Oberauer and M. Oaksford, What must a psychological theory of reasoning explain?, Comment on Barrouillet, Gauffroy, and Lecas, vol.115, pp.773-778, 2008.

K. Oberauer, A. Weidenfeld, and K. Fischer, What makes us believe a conditional? The roles of covariation and causality, Thinking & Reasoning, vol.13, issue.4, pp.340-369, 2007.

K. Oberauer and O. Wilhelm, Effects of directionality in deductive reasoning: I. The comprehension of single relational premises, Journal of Experimental Psychology: Learning, Memory, and Cognition, vol.26, issue.6, pp.1702-1712, 2000.

K. Oberauer and O. Wilhelm, The meaning(s) of conditionals: Conditional probabilities, mental models, and personal utilities, Journal of Experimental Psychology: Learning, Memory, and Cognition, vol.29, pp.680-693, 2003.

I. Orenes and P. N. Johnson-laird, Logic, models, and paradoxical inferences, Mind & Language, vol.27, issue.4, pp.357-377, 2012.

D. E. Over, Deduction and degrees of belief, Behavioral and Brain Sciences, vol.16, pp.361-362, 1993.

D. E. Over, New paradigm psychology of reasoning. Thinking & Reasoning, vol.15, pp.431-438, 2009.

D. E. Over, The paradigm shift in the psychology of reasoning: The debate, 2016.

, Cognitive unconscious and human rationality, pp.79-97

D. E. Over, D. E. Over, and J. Baratgin, The "defective" truth table: Its past, present, and future, pp.15-28, 2017.

D. E. Over and N. Cruz, Probabilistic accounts of conditional reasoning, International handbook of thinking and reasoning, pp.434-450, 2018.

D. Over and N. Cruz, Philosophy and the psychology of conditional reasoning, Advances in Experimental Philosophy of Logic and Mathematics

D. E. Over, J. Evans, . B. St, and S. Elqayam, Conditionals and non-constructive reasoning, Cognition and Conditionals: Probability and Logic in Human Thinking, pp.135-151, 2010.

D. E. Over, C. Hadjichristidis, J. Evans, . B. St, S. J. Handley et al., The probability of causal conditionals, Cognitive Psychology, vol.54, pp.62-97, 2007.

J. Pearl, Probabilistic Reasoning in Intelligent Systems: Networks of Plausible Inference, 1988.

J. Pearl, Causality: Models, reasoning, and inference, 2000.

J. Pearl, Structural counterfactuals: a brief introduction, Cognitive Science, vol.37, pp.977-985, 2013.

E. Peer, L. Brandimarte, S. Samat, and A. Aquisti, Beyond the Turk: Alternative platforms for crowdsourcing behavioral research, Journal of Experimental Social Psychology, vol.70, pp.153-163, 2017.

N. Pfeifer, Contemporary syllogistics: Comparative and quantitative syllogisms, 2006.

, Argumentation in Theorie und Praxis: Philosophie und Didaktik des Argumentierens, pp.57-71

N. Pfeifer and G. D. Kleiter, Coherence and nonmonotonicity in human reasoning, Synthese, vol.146, issue.1-2, pp.93-109, 2005.

N. Pfeifer and G. D. Kleiter, Framing human inference by coherence based probability logic, Journal of Applied Logic, vol.7, pp.206-217, 2009.

N. Pfeifer and G. D. Kleiter, The conditional in mental probability logic, Cognition and conditionals: Probability and logic in human thinking, pp.153-173, 2010.

N. Pfeifer and G. Sanfilippo, Probabilistic squares and hexagons of opposition under coherence, International Journal of Approximate Reasoning, vol.88, pp.282-294, 2017.

N. Pfeifer and R. Stöckle-schobel, Uncertain conditionals and counterfactuals in (non-)causal settings, Proceedings of the EuroAsianpacific Joint Conference on Cognitive Science, pp.651-656, 2015.

G. Politzer and J. Baratgin, Deductive schemas with uncertain premises using qualitative probability expressions, Thinking & Reasoning, vol.22, pp.78-98, 2016.
URL : https://hal.archives-ouvertes.fr/ijn_01293776

G. Politzer and I. A. Noveck, Are conjunction rule violations the result of conversational rule violations, Journal of Psycholinguistic Research, vol.20, issue.2, pp.83-103, 1991.

G. Politzer, D. E. Over, and J. Baratgin, Betting on conditionals. Thinking & Reasoning, vol.16, pp.172-197, 2010.
URL : https://hal.archives-ouvertes.fr/hal-01015797

K. Popper, The logic of scientific discovery, 2002.

E. M. Pothos and J. R. Busemeyer, Can quantum probability provide a new direction for cognitive modeling?, Behavioral and Brain Sciences, vol.36, pp.255-327, 2013.

E. M. Pothos, J. R. Busemeyer, R. M. Shiffrin, and J. M. Yearsley, The rational status of Quantum Cognition, Journal of Experimental Psychology: General, vol.146, issue.7, pp.968-987, 2017.

J. Prado, A. Chadha, and J. R. Booth, The brain network for deductive reasoning: A quantitative meta-analysis of 28 neuroimaging studies, Journal of Cognitive Neuroscience, vol.23, issue.11, pp.3483-3497, 2011.
URL : https://hal.archives-ouvertes.fr/hal-00904046

G. Priest, An introduction to non-classical logic, 2008.

M. Ragni and M. Knauff, A theory and a computational model of spatial reasoning with preferred mental models, Psychological Review, vol.120, issue.3, pp.561-588, 2013.

F. P. Ramsey, Truth and probability, pp.52-94, 1926.

F. P. Ramsey, General propositions and causality, pp.145-163, 1929.

. Reichenbach, The theory of probability, 1949.

L. Rips, Cognitive processes in propositional reasoning, Psychological Review, vol.90, pp.38-71, 1983.

L. J. Rips, The psychology of proof, 1994.

L. J. Rips, Two kinds of reasoning, Psychological Science, vol.12, issue.2, pp.129-134, 2001.

W. S. Robinson, Ecological correlations and the behavior of individuals, American Sociological Review, vol.15, issue.3, pp.351-357, 1950.

A. N. Sanborn and N. Chater, Bayesian brains without probabilities, Trends in Cognitive Sciences, vol.20, issue.12, pp.883-893, 2016.

W. Schroyens, N. Verschueren, W. Schaeken, and G. Ydewalle, Conditional reasoning with negations: Implict and explicit affirmation or denial and the role of contrast classes, Thinking and Reasoning, vol.6, issue.3, pp.221-251, 2000.

B. Schwan and R. Stern, A causal understanding of when and when not to Jeffrey connditionalize. Philosopher's imprint, vol.17, pp.1-21, 2017.

A. Sides, D. Osherson, N. Bonini, and R. Viale, On the reality of the conjunction fallacy, Memory & Cognition, vol.30, pp.191-198, 2002.

H. Singmann and K. C. Klauer, Deductive and inductive conditional inferences: Two modes of reasoning, Thinking & Reasoning, vol.17, issue.3, pp.247-281, 2011.

H. Singmann, K. C. Klauer, and D. E. Over, New normative standards of conditional reasoning and the dual-source model, Frontiers in Psychology, vol.5, p.316, 2014.

N. Skovgaard-olsen, H. Singmann, and K. C. Klauer, The relevance effect and conditionals, Cognition, vol.150, pp.26-36, 2016.

S. A. Sloman, The empirical case for two systems of reasoning, Psychological Bulletin, vol.119, issue.1, pp.3-22, 1996.

S. Sloman, How people think about the world and its alternatives, 2005.

S. A. Sloman, Dual process theories of the social mind, 2014.

S. A. Sloman and D. A. Lagnado, Do we "do, Cognitive Science, vol.29, pp.5-39, 2005.

S. A. Sloman, D. Over, L. Slovak, and J. M. Stibel, Frequency illusions and other fallacies. Organizational Behavior and Humen Decision Processes, vol.91, pp.296-309, 2003.

T. A. Snijders and R. J. Bosker, Multilevel analysis: An introduction to basic and advanced multilevel modeling, 1999.

T. A. Snijders and R. J. Bosker, Multilevel analysis: An introduction to basic and advanced multilevel modeling, 2012.

W. Spohn, A ranking-theoretic approach to conditionals, Cognitive Science, vol.37, issue.6, pp.1074-1106, 2013.

R. Stalnaker, A theory of conditionals, Studies in logical theory, pp.98-112, 1968.

R. Stalnaker, Probability and conditionals, Philosophy of Science, vol.37, pp.64-80, 1970.

K. Stalnaker and R. Jeffrey, Conditionals as random variables, Probability and conditionals: Belief revision and rational decision, pp.31-46, 1994.

K. E. Stanovich, R. F. West, and M. E. Toplak, Myside bias, rational thinking, and intelligence, Psychological Science, vol.22, issue.4, pp.259-264, 2013.

R. Stern, A causal understanding of when and when not to Jeffrey conditionalize. Philosopher's Imprint, vol.17, pp.1-21, 2017.

R. Stern, Talk on dynamic reasoning with embedded conditionals, Third Villa Vigoni trilateral workshop on Human rationality: Probabilistic perspectives. Loveno di, 2017.

R. J. Stevenson and D. E. Over, Deduction from uncertain premises, Journal of Experimental Psychology, vol.48, issue.3, pp.613-643, 1995.

N. Stewart, N. Chater, and G. D. Brown, Decision by sampling, Cognitive Psychology, vol.53, pp.1-26, 2006.

B. Tabachnick and L. S. Fidell, Using multivariate statistics: International edition, 2007.

M. Te-grotenhuis, R. Eisinga, and S. V. Subramanian, Robinson's Ecological Correlations and the Behavior of Individuals: Methodological corrections, International Journal of Epidemiology, vol.40, issue.4, pp.1123-1125, 2011.

K. Tentori, V. Crupi, and S. Russo, On the determinants of the conjunction fallacy: probability vs inductive confirmation, Journal of Experimental Psychology: General, vol.142, pp.235-255, 2013.

K. Tentori, N. Bonini, and D. Osherson, The conjunction fallacy: A misunderstanding about conjunction?, Cognitive Science, vol.28, pp.467-477, 2004.

V. A. Thompson, Interpretational factors in conditional reasoning, Memory and Cognition, vol.22, pp.742-758, 1994.

V. A. Thompson and R. M. Byrne, Reasoning counterfactually: Making inferences about things that didn't happen, Journal of Experimental Psychology: Learning, Memory, and Cognition, vol.28, pp.1154-1170, 2002.

V. A. Thompson and S. C. Johnson, Conflict, metacognition, and analytic thinking, Thinking & Reasoning, vol.20, issue.2, pp.215-244, 2014.

D. Trippas, S. J. Handley, M. F. Verde, and K. Morsanyi, Logic brightens my day: Evidence for implicit sensitivity to logical validity, Journal of Experimental Psychology: Learning, Memory, and Cognition, vol.42, issue.9, pp.1448-1457, 2016.

D. Trippas, V. A. Thompson, and S. J. Handley, When fast logic meets slow belief: Evidence for a parallel-processing model of belief bias, Memory & Cognition, vol.45, issue.4, pp.539-552, 2017.

A. Tversky and D. Kahneman, Extensional versus intuitive reasoning: The conjunction fallacy in probability judgment, Psychological Review, vol.90, pp.293-315, 1983.

A. Tversky and D. J. Köhler, Support theory: A nonextensional representation of subjective probability, Psychological Review, vol.101, issue.4, pp.547-567, 1994.

J. Van-heijenoort, From Frege to Goedel: A source book in mathematical logic, pp.1879-1931, 1967.

J. Van-wijnbergen-huitink, S. Elqayam, and D. E. Over, The probability of iterated conditionals, Cognitive Science, vol.39, issue.4, pp.788-803, 2015.

J. Venn, 1886/1963). The Logic of Chance

N. Verschueren, W. Schaeken, and G. Ydewalle, A dual-process specification of causal conditional reasoning, Thinking & Reasoning, vol.11, issue.3, pp.239-278, 2005.

M. Vidal and J. Baratgin, A psychological study of unconnected conditionals, Journal of Cognitive Psychology, vol.29, issue.6, pp.769-781, 2017.

S. Vineberg, The Stanford Encyclopedia of Philosophy, 2016.

V. Mises and R. , Probability, Statistics, and Truth, 1951.

V. Sydow and M. , Rational and semi-rational explanations of the conjunction fallacy: A polycausal approach, 2017.

, The 39th Annual Meeting of the Cognitive Science Society

P. C. Wason, Reasoning about a rule, Quarterly Journal of Experimental Psychology, vol.20, issue.3, pp.273-281, 1968.

J. Westfall, C. M. Judd, and D. A. Kenny, Statistical power and optimal design in experiments in which samples of participants respond to samples of stimuli, Journal of Experimental Psychology: General, vol.143, issue.5, pp.2020-2045, 2014.

L. Wittgenstain, On certainty, Denis Paul (Transl.), 1991.

J. Zhao and D. Osherson, Updating beliefs in light of uncertain evidence: Descriptive assessment of Jeffrey's rule. Thinking & Reasoning, vol.16, pp.288-307, 2010.

J. Zhao and D. Osherson, Category-based updating, Thinking & Reasoning, vol.20, issue.1, pp.1-15, 2014.