We give sound and complete tableau and sequent calculi for the propositional normal modal logics $4.04, K4B and G O (these logics axe the smallest normal modal logics containing K and the schemata [:]A -+ ODA, DA --+ A and D<)DA --+ (A --+ DA) ; DA -+ D[]A and A -+ D<>A ; DA --+ D[qA and D(D(A --+ D
Cut-free sequent calculi for some tense logics
β Scribed by Ryo Kashima
- Publisher
- Springer Netherlands
- Year
- 1994
- Tongue
- English
- Weight
- 691 KB
- Volume
- 53
- Category
- Article
- ISSN
- 0039-3215
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π SIMILAR VOLUMES
## Abstract Two cutβfree sequent calculi which are conservative extensions of Visser's Formal Propositional Logic (FPL) are introduced. These satisfy a kind of subformula property and by this property the interpolation theorem for FPL are proved. These are analogies to AghaeiβArdeshir's calculi for
In this article, a cut-free system TLMΟ 1 for infinitary propositional modal logic is proposed which is complete with respect to the class of all Kripke frames. The system TLMΟ 1 is a kind of Gentzen style sequent calculus, but a sequent of TLMΟ 1 is defined as a finite tree of sequents in a standar