arXiv subjects
Publications and source records attributed to Simon Lemal.
We prove that the Fischer-Servi logic $\mathsf{IK}$ does not have the (Craig) interpolation property. This is obtained by showing that the corresponding class of modal Heyting algebras lacks the amalgamation property. We also generalize this result to some extensions of the Fischer-Servi logic such as $\mathsf{IT}$, $\mathsf{IK4}$, $\mathsf{IS4}$, and $\mathsf{IGL}$.
We show that the variety of modal lattices has the superamalgamation property. As a consequence, we obtain that the weak positive modal logic has the Craig interpolation property. Our proof employs the recent duality for modal lattices based on modal L-spaces. Moreover, we extend this result to a number of other weak positive modal logics axiomatized by modal axioms corresponding to universal Horn sentences.