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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 Λ-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 Λ-calculi… (More)

- Moreno Falaschi, Hirohisa Seki, Stephen Skeirik, Germán Vidal, Sergio Antoy, GILLES BARTHE +31 others
- 2015

We study cut elimination for a multifocused variant of linear logic in the sequent calculus. The multifocused normal form of proofs yields problems that do not appear in the standard focused system, related to the constraints in grouping rule instances inside focusing phases. We show that cut elimination can be performed in a sensible way even though the… (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)

In intuitionistic sequent calculi, detecting that a sequent is unprovable is often used to direct proof search. This is for instance seen in backward chaining, where an unprovable subgoal means that the proof search must backtrack. In undecidable logics, however, proof search may continue indefinitely, finding neither a proof nor a disproof of a given… (More)

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