Centering and the meaning of conditionals

The centering inference p & q, therefore if p then q is important in reasoning research because it is logically valid for some accounts of conditionals (e. g. the material and the probability conditionals), but not for others (e. g. the inferential conditional, according to which a conditional is true if and only if there is an inferential connection between p and q). We tested participants' acceptance of centering compared to valid and invalid inferences not containing conditionals, varying the presence of an inferential connection and of a common topic of discourse between p and q. Participants' acceptance of centering was more similar to valid inferences than to invalid inferences, and there was no reliable effect of a connection between p and q. Acceptance rates were higher when there was a common topic of discourse, independently of the type of inference. The findings support the probability conditional account.