This paper concerns modal logics of provability -- Gödel-Löb system GL and Solovay logic S -- the smallest and the greatest representation of arithmetical theories in propositional logic respectively.

The thesis that, in a system of natural deduction, the meaning of a logical constant is given by some or all of its introduction and elimination rules has been developed recently in the work of ...

Mastering the art of deduction was once thought to be a singularly human skill, but research has since shown that animals, including chimpanzees, birds, rats, fish and geese, are capable of using a ...

A new study provides the first evidence of transitive inference, the ability to use known relationships to infer unknown relationships, in a nonvertebrate animal: the lowly paper wasp. A new ...

Within the first year of life, children can make transitive inferences about a social hierarchy of dominance. Human infants are capable of deductive problem solving as early as 10 months of age, a new ...

Logical reasoning is complex behaviour, and has often been thought to be limited to animals that have complex nervous systems. But a new study shows that wasps can use a kind of logical deduction, the ...