Geodesic
Semantics for Some Intermediate Logics
Publications de l'Institut Mathématique, _N_S_37 (1985) no. 51, p. 7

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We give semantics for intermediate logics of the form $H+\vee S$, where $\vee S$ is the schema $ \underset{(i,j)\in S}\to\vee(A_i\to A_j) $ and $S$ is a nonempty subset of $\{1,\ldots,n\}^2$. It is proved that such a logic is complete with respect to the class of Kripke frames $(X,R)$ which satisfy the universal closure of the formula $\underset{(i,j),(k,i)\in S}\to\vee x_{ij}Rx_{ki} $
Classification : 03B55 
@article{PIM_1985_N_S_37_51_a1,
     author = {Milan Bo\v{z}i\'c},
     title = {Semantics for {Some} {Intermediate} {Logics}},
     journal = {Publications de l'Institut Math\'ematique},
     pages = {7 },
     publisher = {mathdoc},
     volume = {_N_S_37},
     number = {51},
     year = {1985},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/PIM_1985_N_S_37_51_a1/}
}
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Milan Božić. Semantics for Some Intermediate Logics. Publications de l'Institut Mathématique, _N_S_37 (1985) no. 51, p. 7 . http://geodesic.mathdoc.fr/item/PIM_1985_N_S_37_51_a1/