Canonical extensions of possibility measures to Boolean algebras of conditionals

In this paper we study conditional possibility measures within the algebraic setting of Boolean algebras of conditional events. More precisely, we focus on the possibilistic version of the Strong Conditional Event Problem, introduced for probabilities by Goodman and Nguyen, and solved in finitary terms in a recent paper by introducing the so-called Boolean algebras of conditionals. Our main result shows that every possibility measure on a finite Boolean algebra can be canonically extended to an unconditional possibility measure on the resulting Boolean algebra of conditionals, in such a way that the canonical extension and the conditional possibility, determined in usual terms by any continuous t-norm, coincide on every basic conditional expression.