## Abstract We develop cutβfree calculi of sequents for normal modal logics by using treesequents, which are trees of sequences of formulas. We introduce modal operators corresponding to the ways we move formulas along the branches of such trees, only considering fixed distance movements. Finally,
Modal sequents for normal modal logics
β Scribed by Claudio Cerrato
- Publisher
- John Wiley and Sons
- Year
- 1993
- Tongue
- English
- Weight
- 433 KB
- Volume
- 39
- Category
- Article
- ISSN
- 0044-3050
No coin nor oath required. For personal study only.
β¦ Synopsis
Abstract
We present sequent calculi for normal modal logics where modal and propositional behaviours are separated, and we prove a cut elimination theorem for the basic system K, so as completeness theorems (in the new style) both for K itself and for its most popular enrichments. MSC: 03B45, 03F05.
π SIMILAR VOLUMES
The standard rule of necessitation in systems of natural deduction for the modal logic S4 concludes A from A whenever all assumptions A depends on are modal formulas. This condition prevents the composability and normalization of derivations, and therefore modifications of the rule have been suggest
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The purpose of this paper is to point out an error in KRISTER SEGERBERG'S proof of the completeness of the modal logic R, and to provide a correct proof.2) The correct proofbased on a notion and a strategy suggested by SEOERBERO'S techniquesintroduces a general approach for obtaining completeness th