Niki Pfeifer
Universität Regensburg
Giuseppe Sanfilippo
Università degli Studi di Palermo
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 of the syllogistic Figures I, II, and III, respectively. These results allow to show, for all three Figures, that each traditionally valid syllogism is also valid in our coherence-based probability semantics. Moreover, we interpret the basic syllogistic sentence types by suitable defaults and negated defaults. Thereby, we build a knowledge bridge from our probability semantics of Aristotelian syllogisms to nonmonotonic reasoning. Finally, we show how the proposed semantics can be used to analyze syllogisms involving generalized quantifiers.
Keywords Aristotelian syllogisms  probability semantics   coherence  conditional events  imprecise probability  nonmonotonic reasoning  generalized quantifiers
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Generalized Quantifiers and Natural Language.John Barwise & Robin Cooper - 1981 - Linguistics and Philosophy 4 (2):159--219.
Quantifiers in Language and Logic.Stanley Peters & Dag Westerståhl - 2006 - Oxford, England: Oxford University Press UK.
The Logic of Conditionals.Ernest Adams, Ernest W. Adams, Jaakko Hintikka & Patrick Suppes - 1974 - Journal of Symbolic Logic 39 (3):609-611.

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