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.
Realizability interpretations of logics are given by saying what it means for computational objects of some kind to realize, logical formulae.
Avicenna's Intuition not only set aside important parts of Aristotle's logic, it also differed from Alfarabi's interpretation of that 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.
One of them is treating the correlational flow of information as a sort of combinatorial system by which local information states are combined in syntactic-like ways fitting a particular interpretation of relevance logic.
In both cases, the intended semantics is existential: the Brouwer-Heyting-Kolmogorov interpretation of Intuitionistic Logic (Heyting 1934, Troelstra and van Dalen 1988, van Dalen 1986) and Gödel's provability reading of \(\mathsf{S4}\) (Gödel 1933, Gödel 1938).
