I am very happy to have this opportunity to introduce Luca Vigano's book on Labelled Non-
Classical Logics. I put forward the methodology of labelled deductive systems to the …

This paper surveys a part of the theory ofβ-reduction inλ-calculus which might aptly be
calledperpetual reductions. The theory is concerned withperpetual reduction strategies, ie …

By interactive theorem proving, we mean some arrangement where the machine and a
human user work together interactively to produce a formal proof. There is a wide spectrum …

The LF logical framework codifies a methodology for representing deductive systems, such
as programming languages and logics, within a dependently typed λ-calculus. In this …

One of the most important contributions of A. Church to logic is his invention of the lambda
calculus. We present the genesis of this theory and its two major areas of application: the …

We describe a formalization of the elementary algebra, topology and analysis of finite-
dimensional Euclidean space in the HOL Light theorem prover.(Euclidean space is …

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 …

We present a framework for machine implementation of families of non-classical logics with
Kripke-style semantics. We decompose a logic into two interacting parts, each a natural …

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 paper reports on the MIZAR formalization of the theory of continuous lattices as
presented in Gierz et al.: A Compendium of Continuous Lattices, 1980. By a MIZAR …