Name
Abstract | ||
|---|---|---|
Abstract There is wide support in logic, philosophy, and psychology for the hypothesis that the probability of the indicative conditional of natural language, P ( if A then B ) , is the conditional probability of B given A , P ( B | A ) . We identify a conditional which is such that P ( if A then B ) = P ( B | A ) with de Finettiu0027s conditional event, B | A . An objection to making this identification in the past was that it appeared unclear how to form compounds and iterations of conditional events. In this paper, we illustrate how to overcome this objection with a probabilistic analysis, based on coherence, of these compounds and iterations. We interpret the compounds and iterations as conditional random quantities which, given some logical dependencies, may reduce to conditional events. We show how the inference to B | A from A and B can be extended to compounds and iterations of both conditional events and biconditional events. Moreover, we determine the respective uncertainty propagation rules. Finally, we make some comments on extending our analysis to counterfactuals. |
Year | DOI | Venue |
|---|---|---|
2018 | 10.1016/J.IJAR.2017.10.027 | Int. J. Approx. Reasoning |
Field | DocType | Volume |
Indicative conditional,Discrete mathematics,Strict conditional,Conditional probability distribution,Conditional probability,Conditional independence,Conditional event algebra,Logical biconditional,Counterfactual conditional,Artificial intelligence,Mathematics,Machine learning | Journal | 93 |
Citations | PageRank | References |
4 | 0.49 | 26 |
Authors | ||
4 | ||
Name | Order | Citations | PageRank |
|---|---|---|---|
| Giuseppe Sanfilippo | 1 | 204 | 17.14 |
| Niki Pfeifer | 2 | 74 | 9.14 |
| David Over | 3 | 11 | 4.13 |
| Angelo Gilio | 4 | 419 | 42.04 |