Realizability interpretations of logics are given by saying what it means for computational objects of some kind to realize, logical formulae.
In Logic Without Metaphysics (1957) he defended a naturalistic interpretation of logic, denying the ontological necessity of logico-mathematical principles and arguing that they must be understood according to their function in specific inquiries.
But it does not fit into Heyting's original interpretation of logic in terms of intentions directed at constructions and the fulfillment of such intentions either.
Clinicians vary in their interpretations of this logic and often localization of such clinical definitions inhibits the incorporation of such logic into decision support rules.
As Jack Meiland (1976) construes Erdmann's philosophy of logic, the psychological interpretation of logical principles is meant to explain why we cannot conceive of radically different logical systems.
Avicenna's Intuition not only set aside important parts of Aristotle's logic, it also differed from Alfarabi's interpretation of that logic.
Heyting himself spoke simply of the "interpretation" (1958A, 107; 1974, 87) or "the intuitionistic interpretation" (1958A, 110) of logic.
Another difficult problem came from various special fields and concerned the reistic interpretation of mathematics, logic, semantics, psychology sociology and the humanities.
It forms a semantic interpretation of the logic elements, while ensuring the integrity (holistic and entanglement) of the coverage of the phenomenon under investigation.
In the late thirties, at least from 1938 on, he developed as a response to Gentzen's proof his own special interpretation of intuitionistic logic and arithmetic, what came to be known as the Dialectica interpretation.
Models for the interpretation of modal logic consist of a pointed set (i.e., a set with a designated member) of possible worlds, an accessibility relation, and a valuation function.
