This paper outlines a theory and computer implementation of causal meanings and reasoning. The meanings depend on possibilities, and there are four weak causal relations: A causes B, A prevents B, A allows B, and A allows not-B, and two stronger relations of cause and prevention. Thus, A causes B corresponds to three possibilities: A and B, not-A and B, and not-A and not-B, with the temporal constraint that B does not precede A; and the stronger relation conveys only the first and last of these possibilities. Individuals represent these relations in mental models of what is true in the various possibilities. The theory predicts a number of phenomena, and, contrary to many accounts, it implies that the meaning of causation is not probabilistic, differs from the meaning of enabling conditions, and does not depend on causal powers or mechanisms. The theory also implies that causal deductions do not depend on schemas or rules.