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 ...
Bar Induction occupies a central place in Brouwerian mathematics. This note is concerned with the strength of Bar Induction on the basis of Constructive ZermeloFraenkel Set Theory...
This paper presents mathematical results that can sometimes be used to simplify the task of reasoning about a default theory, by \splitting it into parts." These so-called Sp...
In this paper we show that an arbitrary propositional theory, when interpreted under the answer sets semantics (called Equilibrium Logic for this general syntax), can always be re...
A definitional extension LNGMIt of the Calculus of Inductive Constructions (CIC), that underlies the proof assistant Coq, is presented that allows also to program with nested dat...