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. 
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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/

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