The new probabilistic/Bayesian paradigm in the psychology of reasoning will be further developed in the proposed research. In the older binary paradigm, people’s beliefs, e.g. about a conditional if A then B, are classified with only two truth values, true or false, e.g. in classic truth table studies in which participants have to classify if A then B as true or false given A and B as either true or false. We will explore the implication of the new paradigm that the conditional and a bet on it have a third value, termed void, when A is false. Further, more refined judgments will also occur according to the new paradigm. Beliefs can be held with varying degrees of confidence, or subjective probability and uncertainty in technical terms, and the new paradigm implies that these judgments will affect reasoning. We will investigate the actual effect of confidence judgments on conditionals and also other connectives: negation, conjunction, disjunction, the material conditional, and the biconditional. It is highly plausible that cultural differences can affect people’s confidence judgments, and we will explore whether such differences can be found when European and Japanese participants are compared.