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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. We first show how sequent calculi for intuitionistic proposition logic, and in particular the G4ip calculus of Vorob'ev, Hudelmaier, and Dyckhoff can be represented as a complete proof calculus that nevertheless contains no… (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)

We study cut elimination for a multifocused variant of full linear logic in the sequent calculus. The multifocused normal form of proofs yields problems that do not appear in a standard focused system, related to the constraints in grouping rule instances in 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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