Geodesic
Weak interpolation in extensions of the logics $S4$ and $K4$
Algebra i logika, Tome 47 (2008) no. 6, pp. 705-722

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Conditions are specified which are necessary and sufficient for a logic over $K4$ to possess the weak interpolation property. For this goal to be met, simple transitive modal algebras are described, and we establish a criterion for the class of such algebras to be amalgamable. For extensions of $K4$, the weak interpolation property is proved decidable.
Keywords: weak interpolation property, modal logic, amalgamability. 
@article{AL_2008_47_6_a2,
     author = {A. V. Karpenko},
     title = {Weak interpolation in extensions of the logics $S4$ and~$K4$},
     journal = {Algebra i logika},
     pages = {705--722},
     publisher = {mathdoc},
     volume = {47},
     number = {6},
     year = {2008},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/AL_2008_47_6_a2/}
}
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A. V. Karpenko. Weak interpolation in extensions of the logics $S4$ and $K4$. Algebra i logika, Tome 47 (2008) no. 6, pp. 705-722. http://geodesic.mathdoc.fr/item/AL_2008_47_6_a2/