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Square of opposition under coherence

In M. B. Ferraro, P. Giordani, B. Vantaggi, M. Gagolewski, P. Grzegorzewski, O. Hryniewicz & María Ángeles Gil (eds.), Soft Methods for Data Science. pp. 407-414 (2017)

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  1. Conditionals, Counterfactuals, and Rational Reasoning: An Experimental Study on Basic Principles.Leena Tulkki & Niki Pfeifer - 2017 - Minds and Machines 27 (1):119-165.
    We present a unified approach for investigating rational reasoning about basic argument forms involving indicative conditionals, counterfactuals, and basic quantified statements within coherence-based probability logic. After introducing the rationality framework, we present an interactive view on the relation between normative and empirical work. Then, we report a new experiment which shows that people interpret indicative conditionals and counterfactuals by coherent conditional probability assertions and negate conditionals by negating their consequents. The data support the conditional probability interpretation of conditionals and the (...)
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  • Probability Semantics for Aristotelian Syllogisms.Niki Pfeifer & Giuseppe Sanfilippo - manuscript
    We present a coherence-based probability semantics for (categorical) Aristotelian syllogisms. For framing the Aristotelian syllogisms as probabilistic inferences, we interpret basic syllogistic sentence types A, E, I, O by suitable precise and imprecise conditional probability assessments. Then, we define validity of probabilistic inferences and probabilistic notions of the existential import which is required, for the validity of the syllogisms. Based on a generalization of de Finetti's fundamental theorem to conditional probability, we investigate the coherent probability propagation rules of argument forms (...)
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