Psychological research on people’s understanding of natural language connectives has traditionally used truth table tasks, in which participants evaluate the truth or falsity of a compound sentence given the truth or falsity of its components in the framework of propositional logic. One perplexing result concerned the indicative conditional if A then C which was often evaluated as true when A and C are true, false when A is true and C is false but irrelevant“ (devoid of value) when A is (...) false (whatever the value of C). This was called the “psychological defective table of the conditional.” Here we show that far from being anomalous the “defective” table pattern reveals a coherent semantics for the basic connectives of natural language in a trivalent framework. This was done by establishing participants’ truth tables for negation, conjunction, disjunction, conditional, and biconditional, when they were presented with statements that could be certainly true, certainly false, or neither. We review systems of three-valued tables from logic, linguistics, foundations of quantum mechanics, philosophical logic, and artificial intelligence, to see whether one of these systems adequately describes people’s interpretations of natural language connectives. We find that de Finetti’s (1936/1995) three-valued system is the best approximation to participants’ truth tables. (shrink)

Causal induction in the real world often has to be quick and efficient as well as accurate. We propose that people use two different frames to achieve these goals. The A-frame consists of heuristic processes that presuppose rarity and can detect causally relevant factors quickly. The B-frame consists of analytic processes that can be highly accurate in detecting actual causes. Our dual frame theory implies that several factors affect whether people use the A-frame or the B-frame in causal induction: among (...) these are symmetrical negation, intervention and commitment. This theory is tested and sustained in two experiments. The results also provide broad support for dual process accounts of human thinking in general. (shrink)