# Conjunction of Conditional Events and T-norms

## TL;DR

This paper explores the connection between conjunctions of conditional events and Frank t-norms, demonstrating their equivalence in various cases and analyzing coherence conditions, especially for Lukasiewicz t-norm.

## Contribution

It establishes a formal link between conjunctions of conditional events and Frank t-norms, including coherence conditions for Lukasiewicz t-norm.

## Key findings

- Conjunctions coincide with Frank t-norms like Product, Minimum, and Lukasiewicz in coherence.
- Counterexample shows Lukasiewicz t-norm may lead to incoherent assessments.
- Conditions for coherence with Lukasiewicz t-norm are provided.

## 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.