In 1933 Gödel introduced a calculus of provability (also known as modal logic S4) and left
open the question of its exact intended semantics. In this paper we give a solution to this …

We present the linear type theory λΠ⊸ &⊤ as the formal basis for LLF, a conservative
extension of the logical framework LF. LLF combines the expressive power of dependent …

Starting from a denotational semantics of the eager untyped lambda-calculus with explicit
runtime errors, the standard collecting semantics is defined as specifying the strongest …

The lambda-Pi-calculus allows to express proofs of minimal predicate logic. It can be
extended, in a very simple way, by adding computation rules. This leads to the lambda-Pi …

Negative facts get a bad press. One reason for this is that it is not clear what negative facts
are. We provide a theory of negative facts on which they are no stranger than positive atomic …

We define a generic notion of cut that applies to many first-order theories. We prove a
generic cut elimination theorem showing that the cut elimination property holds for all …

Type Theory (Stanford Encyclopedia of Philosophy) SEP home page Stanford Encyclopedia of
Philosophy Browse Table of Contents What's New Random Entry Chronological Archives About …

In this paper, we propose to extend the Barendregt Cube by generalisingβ-reduction and by
adding definition mechanisms. Generalised reduction allows contracting more visible …

This is the first of a series of three articles devoted to the conceptual problem of identifying
the natural notions of computability at higher types (over the natural numbers) and …

We describe a type system for the linear-algebraic λ-calculus. The type system accounts for
the linear-algebraic aspects of this extension of λ-calculus: it is able to statically describe the …