6533b85cfe1ef96bd12bcbab
RESEARCH PRODUCT
Centering and Compound Conditionals under Coherence
Niki PfeiferDavid E. OverGiuseppe SanfilippoAngelo Giliosubject
Discrete mathematicsIndicative conditionalcenteringSettore MAT/06 - Probabilita' E Statistica Matematica05 social sciencesClassical logicConditional probabilityInference02 engineering and technologyCoherence (philosophical gambling strategy)p-entailmentn-conditional event050105 experimental psychologycoherenceLogical biconditionalp-validity0202 electrical engineering electronic engineering information engineeringbiconditional event020201 artificial intelligence & image processing0501 psychology and cognitive sciencesProbabilistic analysis of algorithmsArithmeticMathematicsEvent (probability theory)Conditionaldescription
There is wide support in logic , philosophy , and psychology for the hypothesis that the probability of the indicative conditional of natural language, \(P(\textit{if } A \textit{ then } B)\), is the conditional probability of B given A, P(B|A). We identify a conditional which is such that \(P(\textit{if } A \textit{ then } B)= P(B|A)\) with de Finetti’s 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 sometimes reduce to conditional events, given logical dependencies. We also show, for the first time, how to extend the inference of centering for conditional events, inferring B|A from the conjunction A and B, to compounds and iterations of both conditional events and biconditional events, B||A, and generalize it to n-conditional events.
| year | journal | country | edition | language |
|---|---|---|---|---|
| 2016-07-30 |