The Psychology of Uncertainty and Three-Valued Truth Tables.

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 which was often evaluated as true when and are true, false when is true and is false but irrelevant" (devoid of value) when is false (whatever the value of ). This was called the "psychological defective table of the conditional.

The class inclusion question: a case study in applying pragmatics to the experimental study of cognition.

For more than 70 years, Piaget's class-inclusion task (given, e.g., five asters and three tulips, the child is asked whether "there are more asters or more flowers") has been the object of experimental investigation.

Preadolescents Solve Natural Syllogisms Proficiently.

"Natural syllogisms" are arguments formally identifiable with categorical syllogisms that have an implicit universal affirmative premise retrieved from semantic memory rather than explicitly stated. Previous studies with adult participants (Politzer, 2011) have shown that the rate of success is remarkably high. Because their resolution requires only the use of a simple strategy (known as ecthesis in classic logic) and an operational use of the concept of inclusion (the recognition that an element that belongs to a subset must belong to the set but not vice versa), it was hypothesized that these syllogisms would be within the grasp of non-adult participants, provided they have acquired the notion of deductive validity.

No problem for Aristotle's subject and predicate.

It is argued that, in the traditional subject-predicate sentence, two interpretations of the subject term coexist, one intensional and the other extensional, which explains the superficial difference between the traditional S-P relation and the predication of predicate logic. Data from psychological studies of syllogistic reasoning support the view that the contrast between predicate and argument is carried over to the traditional S-P sentence.

The interpretation of classically quantified sentences: a set-theoretic approach.

We present a set-theoretic model of the mental representation of classically quantified sentences (All P are Q, Some P are Q, Some P are not Q, and No P are Q). We take inclusion, exclusion, and their negations to be primitive concepts. We show that although these sentences are known to have a diagrammatic expression (in the form of the Gergonne circles) that constitutes a semantic representation, these concepts can also be expressed syntactically in the form of algebraic formulas.

Deductive reasoning from uncertain conditionals.

This paper begins with a review of the literature on plausible reasoning with deductive arguments containing a conditional premise. There is concurring evidence that people presented with valid conditional arguments such as Modus Ponens and Modus Tollens generally do not endorse the conclusion, but rather find it uncertain, in case (1) the plausibility of the major conditional premise is debatable, (2) the major conditional premise is formulated in frequentist or probabilistic terms, or (3) an additional premise introduces uncertainty about the major conditional premise. This third situation gives rise to non-monotonic effects by a mechanism that can be characterized as follows: the reasoner is invited to doubt the major conditional premise by doubting the satisfaction of a tacit condition, which is necessary for the consequent to occur.