Three characterizations of strict coherence on infinite-valued events

TL;DR

This paper explores three different characterizations of strict coherence in infinite-valued Łukasiewicz logic, employing geometrical, measure-theoretical, and logical methods to deepen the understanding of probability on many-valued events.

Contribution

It introduces three novel characterizations of strict coherence in infinite-valued logic, enhancing the logical foundations of probability theory for many-valued events.

Findings

Provides geometrical characterization of strict coherence

Offers measure-theoretical perspective on strict coherence

Develops logical framework for understanding strict coherence

Abstract

This paper builds on a recent article co-authored by the present author, H. Hosni and F. Montagna. It is meant to contribute to the logical foundations of probability theory on many-valued events and, specifically, to a deeper understanding of the notion of strict coherence. In particular, we will make use of geometrical, measure-theoretical and logical methods to provide three characterizations of strict coherence on formulas of infinite-valued {\L}ukasewicz logic