A Semantic Approach to Illative Combinatory Logic

Lukasz Czajka
This work introduces the theory of illative combinatory algebras, which is closely related to systems of illative combinatory logic. We thus provide a semantic interpretation for a formal framework in which both logic and computation may be expressed in a unified manner. Systems of illative combinatory logic consist of combinatory logic extended with constants and rules of inference intended to capture logical notions. Our theory does not correspond strictly to any traditional system, but draws...