The consequences of Dubois and Prade's minimum specificity principle are shown under a continuous t-norm T, when dealing with conditioning and independence in possibility theory. The minimum specificity principle singles out a particular sub-class of T-conditional possibilities (referred to as T-DP-conditional possibilities) adhering to a suitable axiomatic definition that relies on the residuum of T. Such a sub-class differentiates from the larger class of T-conditional possibilities in terms of non-closure with respect to pointwise limits, non-connectedness of extension sets, and Kolmogorov-like representation. We then switch to coherence for a partial assessment in both frameworks, highlighting that, under T-DP-conditioning, coherence of the global assessment cannot be characterized in terms of coherence on every finite sub-family. Finally, both for T-conditioning and T-DP-conditioning, we introduce an independence notion that implies logical independence and we investigate the differences due to minimum specificity.

Consequences of the minimum specificity principle on conditioning and on independence in possibility theory

Giulianella Coletti;Davide Petturiti
;
2023

Abstract

The consequences of Dubois and Prade's minimum specificity principle are shown under a continuous t-norm T, when dealing with conditioning and independence in possibility theory. The minimum specificity principle singles out a particular sub-class of T-conditional possibilities (referred to as T-DP-conditional possibilities) adhering to a suitable axiomatic definition that relies on the residuum of T. Such a sub-class differentiates from the larger class of T-conditional possibilities in terms of non-closure with respect to pointwise limits, non-connectedness of extension sets, and Kolmogorov-like representation. We then switch to coherence for a partial assessment in both frameworks, highlighting that, under T-DP-conditioning, coherence of the global assessment cannot be characterized in terms of coherence on every finite sub-family. Finally, both for T-conditioning and T-DP-conditioning, we introduce an independence notion that implies logical independence and we investigate the differences due to minimum specificity.
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11391/1552533
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