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28Mental probability logicBehavioral and Brain Sciences 32 (1): 98-99. 2009.We discuss O&C's probabilistic approach from a probability logical point of view. Specifically, we comment on subjective probability, the indispensability of logic, the Ramsey test, the consequence relation, human nonmonotonic reasoning, intervals, generalized quantifiers, and rational analysis
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13Experiments on Aristotle’s ThesisThe Monist 95 (2): 223-240. 2012.Two experiments (N1 = 141, N2 = 40) investigate two versions of Aristotle’s Thesis for the first time. Aristotle’s Thesis is a negated conditional, which consists of one propositional variable with a negation either in the antecedent (version 1) or in the consequent (version 2). This task allows us to infer if people interpret indicative conditionals as material conditionals or as conditional events. In the first experiment I investigate between-participants the two versions of Aristotle’s Thesi…Read more
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26Transitivity in coherence-based probability logicJournal of Applied Logic 14 46-64. 2016.We study probabilistically informative (weak) versions of transitivity by using suitable definitions of defaults and negated defaults in the setting of coherence and imprecise probabilities. We represent p-consistent sequences of defaults and/or negated defaults by g-coherent imprecise probability assessments on the respective sequences of conditional events. Moreover, we prove the coherent probability propagation rules for Weak Transitivity and the validity of selected inference patterns by pro…Read more
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27Rational argumentation under uncertaintyIn G. Kreuzbauer, N. Gratzl & E. Hiebl (eds.), Persuasion Und Wissenschaft: Aktuelle Fragestellungen von Rhetorik Und Argumentationstheorie, Lit. pp. 181--191. 2007.Common sense arguments are practically always about incomplete and uncertain information. We distinguish two aspects or kinds of uncertainty. The one is defined as a persons’ uncertainty about the truth of a sentence. The other uncertainty is defined as a persons’ uncertainty of his assessment of the truth of a sentence. In everyday life argumentation we are often faced with both kinds of uncertainty which should be distinguished to avoid misunderstandings among discussants. The paper presents a…Read more
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41Human reasoning with imprecise probabilities: Modus ponens and Denying the antecedentIn Niki Pfeifer & G. D. Kleiter (eds.), Proceedings of the 5 T H International Symposium on Imprecise Probability: Theories and Applications, . pp. 347--356. 2007.The modus ponens (A -> B, A :. B) is, along with modus tollens and the two logically not valid counterparts denying the antecedent (A -> B, ¬A :. ¬B) and affirming the consequent, the argument form that was most often investigated in the psychology of human reasoning. The present contribution reports the results of three experiments on the probabilistic versions of modus ponens and denying the antecedent. In probability logic these arguments lead to conclusions with imprecise probabilities. In t…Read more
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18Coherence and Nonmonotonicity in Human ReasoningSynthese 146 (1-2): 93-109. 2005.Nonmonotonic reasoning is often claimed to mimic human common sense reasoning. Only a few studies, though, have investigated this claim empirically. We report four experiments which investigate three rules of SYSTEMP, namely the AND, the LEFT LOGICAL EQUIVALENCE, and the OR rule. The actual inferences of the subjects are compared with the coherent normative upper and lower probability bounds derived from a non-infinitesimal probability semantics of SYSTEM P. We found a relatively good agreement …Read more
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7Systematic rationality norms provide research roadmaps and clarityBehavioral and Brain Sciences 34 (5): 263-264. 2011.Normative theories like probability logic provide roadmaps for psychological investigations. They make theorizing precise. Therefore, normative considerations should not be subtracted from psychological research. I explain why conditional elimination inferences involve at least two norm paradigms; why reporting agreement with rationality norms is informative; why alleged asymmetric relations between formal and psychological theories are symmetric; and I discuss the arbitration problem.
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89Towards a probability logic based on statistical reasoningIn Niki Pfeifer & G. D. Kleiter (eds.), Towards a probability logic based on statistical reasoning, . pp. 2308--2315. 2006.Logical argument forms are investigated by second order probability density functions. When the premises are expressed by beta distributions, the conclusions usually are mixtures of beta distributions. If the shape parameters of the distributions are assumed to be additive (natural sampling), then the lower and upper bounds of the mixing distributions (P´olya-Eggenberger distributions) are parallel to the corresponding lower and upper probabilities in conditional probability logic
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42Nonmonotonicity and human probabilistic reasoningIn Niki Pfeifer & G. D. Kleiter (eds.), Proceedings of the 6 T H Workshop on Uncertainty Processing, . pp. 221--234. 2003.Nonmonotonic logics allow—contrary to classical (monotone) logics— for withdrawing conclusions in the light of new evidence. Nonmonotonic reasoning is often claimed to mimic human common sense reasoning. Only a few studies, though, have investigated this claim empirically. system p is a central, broadly accepted nonmonotonic reasoning system that proposes basic rationality postulates. We previously investigated empirically a probabilistic interpretation of three selected rules of system p. We fo…Read more