Weak Implication in Terms of Conditional Uncertainty Measures

Authors:
Giulianella Coletti;Romano Scozzafava;Barbara Vantaggi
Affiliations:
Università di Perugia, Italy;Università di Roma "La Sapienza", Italy;Università di Roma "La Sapienza", Italy
Venue:
ECSQARU '07 Proceedings of the 9th European Conference on Symbolic and Quantitative Approaches to Reasoning with Uncertainty
Year:
2007

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Abstract

We define weak implication $H \longmapsto_{\varphi} E$ ("H weakly implies E under $\mathit{\varphi}$") through the relation $\mathit{\varphi}(E|H)$ = 1, where $\mathit{\varphi}$ is a (coherent) conditional uncertainty measure. By considering various such measures with different levels of generality, we get different sets of "inferential rules", that correspond to those of default logic when $\mathit{\varphi}$ reduces to a conditional probability.