Information algebras of coherent sets of gambles in general possibility spaces

TL;DR

This paper demonstrates that coherent sets of gambles can be embedded into an information algebra framework, providing new insights into their algebraic and logical structure and linking them to other computer science formalisms.

Contribution

It introduces a novel algebraic perspective on desirability and imprecise probabilities by embedding coherent sets of gambles into an information algebra in general possibility spaces.

Findings

Coherent sets of gambles can be embedded into information algebra.

Provides both domain-free and labeled views of the algebra.

Connects desirability to formal structures in computer science.

Abstract

In this paper, we show that coherent sets of gambles can be embedded into the algebraic structure of information algebra. This leads firstly, to a new perspective of the algebraic and logical structure of desirability and secondly, it connects desirability, hence imprecise probabilities, to other formalism in computer science sharing the same underlying structure. Both the domain-free and the labeled view of the information algebra of coherent sets of gambles are presented, considering general possibility spaces.