On superintuitionistic logics as fragments of proof logic extensions

Studia Logica 45 (1):77 - 99 (1986)
Coming fromI andCl, i.e. from intuitionistic and classical propositional calculi with the substitution rule postulated, and using the sign to add a new connective there have been considered here: Grzegorozyk's logicGrz, the proof logicG and the proof-intuitionistic logicI set up correspondingly by the calculiFor any calculus we denote by the set of all formulae of the calculus and by the lattice of all logics that are the extensions of the logic of the calculus, i.e. sets of formulae containing the axioms of and closed with respect to its rules of inference. In the logiclG the sign is decoded as follows: A = (A & A). The result of placing in the formulaA before each of its subformula is denoted byTrA. The maps are defined (in the definitions of x and the decoding of is meant), by virtue of which the diagram is constructed.
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References found in this work BETA
Krister Segerberg (1971). An Essay in Classical Modal Logic. Uppsala, Filosofiska Föreningen Och Filosofiska Institutionen Vid Uppsala Universitet.

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Leo Esakia, Mamuka Jibladze & Dito Pataraia (2000). Scattered toposes. Annals of Pure and Applied Logic 103 (1-3):97-107.

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