Taus Brock-Nannestad

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Natural deduction for intuitionistic linear logic is known to be full of non-deterministic choices. In order to control these choices, we combine ideas from intercalation and focusing to arrive at the calculus of focused natural deduction. The calculus is shown to be sound and complete with respect to first-order intuitionistic linear natural deduction and(More)
We revisit intuitionistic proof theory from the point of view of the formula isomorphisms arising from high-school identities. Using a representation of formulas as exponential polynomials, we first observe that invertible proof rules of sequent calculi for intuitionistic proposition logic correspond to equations using high-school identities, and that hence(More)
We investigate the control of evaluation strategies in a variant of the &#923;-calculus derived through the Curry-Howard correspondence from <b><i>LJF</i></b>, a sequent calculus for intuitionistic logic implementing the focusing technique. The proof theory of focused intuitionistic logic yields a single calculus in which a number of known &#923;-calculi(More)
In the paper " Structural Cut Elimination " , Pfenning gives a proof of the admissibility of cut for intuitionistic and classical logic. The proof is remarkable in that it does not rely on difficult termination metrics, but rather a nested lexicographical induction on the structure of formulas and derivations. A crucial requirement for this proof to go(More)
We discuss the extension of the LF logical framework with operators for manipulating worlds, as found in hybrid logics or in the HLF framework. To overcome the restrictions of HLF, we present a more general approach to worlds in LF, where the structure of worlds can be described in an explicit way. We give a canonical presentation for this system and(More)