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
Classically complete modal relevant logics
β Scribed by Edwin D. Mares
- Publisher
- John Wiley and Sons
- Year
- 1993
- Tongue
- English
- Weight
- 674 KB
- Volume
- 39
- Category
- Article
- ISSN
- 0044-3050
No coin nor oath required. For personal study only.
β¦ Synopsis
Abstract
A variety of modal logics based on the relevant logic R are presented. Models are given for each of these logics and completeness is shown. It is also shown that each of these logics admits Ackermann's rule Ξ³ and as a corollary of this it is proved that each logic is a conservative extension of its counterpart based on classical logic, hence we call them βclassically completeβ. MSC: 03B45, 03B46.
π SIMILAR VOLUMES
ON SOME COMPLETENESS THEOREMS IN MODAL LOGIC1) by D. MAKINSON in Oxford (England)
## Abstract In previous works, we presented a modification of the usual possible world semantics by introducing an independent temporal structure in each world and using accessibility functions to represent the relation among them. Different properties ofthe accessibility functions (being injective