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Purity through Unravelling
 TECHNISCHE UNIVERSITÃ„T DRESDEN
, 2005
"... We divide attempts to give the structural proof theory of modal logics into two kinds, those pure formulations whose inference rules characterise modality completely by means of manipulations of boxes and diamonds, and those labelled formulations that leverage the use of labels in giving inferen ..."
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We divide attempts to give the structural proof theory of modal logics into two kinds, those pure formulations whose inference rules characterise modality completely by means of manipulations of boxes and diamonds, and those labelled formulations that leverage the use of labels in giving inference rules. The widespread adoption of labelled formulations is driven by their ability to model features of the model theory of modal logic in its proof theory. We describe
Structures and Deduction  the Quest for the Essence of Proofs (satellite workshop of ICALP 2005)
, 2005
"... Derivations, Equational Logic and Interpolation p. 173 Elaine Pimentel, Simona Ronchi della Rocca and Luca Roversi: Intersection Types: a ProofTheoretical Approach p. 189 Joao Rasga: A Cut Elimination in Propositional Based Logics p. 205 Beyond Deduction Modulo Claude Kirchner INRIA & LO ..."
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Derivations, Equational Logic and Interpolation p. 173 Elaine Pimentel, Simona Ronchi della Rocca and Luca Roversi: Intersection Types: a ProofTheoretical Approach p. 189 Joao Rasga: A Cut Elimination in Propositional Based Logics p. 205 Beyond Deduction Modulo Claude Kirchner INRIA & LORIA Nancy, France From Deep Inference to Proof Nets Universitat des Saarlandes  Informatik  Programmiersysteme Postfach 15 11 50  66041 Saarbrucken  Germany http://www.ps.unisb.de/~lutz Abstract. This paper shows how derivations in (a variation of) SKS can be translated into proof nets. Since an SKS derivation contains more information about a proof than the corresponding proof net, we observe a loss of information which can be understood as "eliminating bureaucracy ". Technically this is achieved by cut reduction on proof nets. As an intermediate step between the two extremes, SKS derivations and proof nets, we will see nets representing derivations in "Formalism A".
Noncommutative proof construction: a constraintbased approach
"... This work presents a computational interpretation of the construction process for cyclic (CyLL) and noncommutative (NL) sequential proofs. We assume a proof construction paradigm, based on a normalisation procedure, known as focussing which manages efficiently the nondeterminism of the constructio ..."
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This work presents a computational interpretation of the construction process for cyclic (CyLL) and noncommutative (NL) sequential proofs. We assume a proof construction paradigm, based on a normalisation procedure, known as focussing which manages efficiently the nondeterminism of the construction. Similarly to the commutative case, a new formulation of focussing for NL is used to introduce a general constraintbased technique in order to deal with partial information during proof construction. In particular, the procedure develops through construction steps propagating constraints in intermediate objects called abstract proofs. 1