Maria Emilia Maietti

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There are several kinds of linear typed calculus in the literature, some with their associated notion of categorical model. Our aim in this paper is to systematise the relationship between three of these linear typed calculi and their models. We point out that mere soundness and completeness of a linear typed calculus with respect to a class of categorical(More)
We study the proof-theory of co-Heyting algebras and present a calculus of continuations typed in the disjunctive–subtractive fragment of dual intuitionistic logic. We give a single-assumption multiple-conclusions Natural Deduction system NJ for this logic: unlike the best-known treatments of multiple-conclusion systems (e.g., Parigot’s λ−μ calculus, or(More)
Suppose in an arithmetic unverse we have two predicates φ and ψ for natural numbers, satisfying a base case φ(0) → ψ(0) and an induction step that, for generic n, the hypothesis φ(n) → ψ(n) allows one to deduce φ(n+ 1) → ψ(n+ 1). Then it is already true in that arithmetic universe that (∀n)(φ(n) → ψ(n)). This is substantially harder than in a topos, where(More)
In this paper we analyze an extension of Martin-Löf’s intensional set theory by means of a set contructor P such that the elements of P(S) are the subsets of the set S. Since it seems natural to require some kind of extensionality on the equality among subsets, it turns out that such an extension cannot be constructive. In fact we will prove that this(More)