Theory interpretation is a logical technique for relating one axiomatic theory to another with important applications in mathematics and computer science as well as in logic itself...
We illustrate the use of intersection types as a semantic tool for showing properties of the lattice of -theories. Relying on the notion of easy intersection type theory we succes...
Propositional type theory, first studied by Henkin, is the restriction of simple type theory to a single base type that is interpreted as the set of the two truth values. We show ...
Abstract. We present a formal treatment of normalization by evaluation in type theory. The involved semantics of simply-typed λ-calculus is exactly the simply typed fragment of th...
This paper provides a unifying axiomatic account of the interpretation of recursive types that incorporates both domain-theoretic and realizability models as concrete instances. O...