Conjunction of Conditional Events and T-norms

Abstract

We study the relationship between a notion of conjunction among conditional events, introduced in recent papers, and the notion of Frank t-norm. By examining different cases, in the setting of coherence, we show each time that the conjunction coincides with a suitable Frank t-norm. In particular, the conjunction may coincide with the Product t-norm, the Minimum t-norm, and Lukasiewicz t-norm. We show by a counterexample, that the prevision assessments obtained by Lukasiewicz t-norm may be not coherent. Then, we give some conditions of coherence when using Lukasiewicz t-norm.

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Cited by in corpus (5)

• First measurement of large area jet transverse momentum spectra in heavy-ion collisions
• Probabilities of conditionals and previsions of iterated conditionals
• Compound conditionals, Fréchet-Hoeffding bounds, and Frank t-norms
• Algebraic aspects and coherence conditions for conjoined and disjoined conditionals
• Interpreting connexive principles in coherence-based probability logic