A semantic theory of deductive reasoning

A theory of deductive reasoning is proposed which is based on the ''mental model'' theory of Johnson-Laird. The theory is developed by applying the central postulate of model semantics consequently: Symbolic propositions are interpreted by mentally constructing states of affairs which in themselves are not symbolic. ''Symbolic extensions'' in mental models are criticized for violating this postulate. They are not necessary in the new theory. Deductive reasoning rests on the mental construction of structures of objects, events and regions in a possible world which are in accordance with the truth conditions of the premises. Logical truth emerges out of the geometrical restrictions of a semantic space which serves as the medium for mental models. Syllogistic and propositional logic are discussed as examples to illustrate this assumptions. Finally, some empirical consequences are discussed which in part deviate from Johnson-Laird's theory.